Crossing the border overland into Jordan from Saudi Arabia is nigh on impossible for non-residents and travel to Iraq is curently on hold, so most travellers generally come overland from Syria or Israel & the Palestinian Territories, or by ferry from Egypt. However, there are three important things to note:
Any indication of travel to/from Israel & the Palestinian Territories will mean that you cannot enter Syria, Lebanon and most other Middle Eastern countries, although Jordan is OK.
All travellers who intend to travel to Syria should ensure they obtain a visa for Syria before coming to Jordan.
Jordanian visas are not available at the Israel/Jordan border at King Hussein Bridge (though they are available at other crossings)
Most travellers arrive in Jordan by bus or service taxi if travelling overland, although it's no problem bringing your own car or motorcycle.
Content
Iraq
Israel & the palestinian territories
Border crossings
Wadi araba
Bus
Car & motorcycle
Saudi Arabia
Syria
Bus
Service taxi
Train
Iraq
Travel to Iraq is not recommended at the present. Land transport crosses at the al-Karama/Tarbil border post, which is located 330km from Amman. Jordan Regular Transport (4622652) at Abdali bus station in Amman currently operates service taxis and minibuses to Baghdad, mostly for Iraqi citizens and using Iraqi drivers. Services leave Amman at midnight in order to get to the border at dawn. Vehicles then travel in convoys for safety into the notorious 'Sunni triangle', passing Fallujah before (in sha'Allah) arriving in Baghdad. A seat in a service taxi costs JD25 and JD15 in a minibus. A private car should cost around JD140.

Israel & the palestinian territories
Since the historic peace treaty between Jordan and Israel & the Palestinian Territories was signed in 1994, three border crossings have opened to foreigners - King Hussein Bridge, Sheikh Hussein Bridge and Wadi Araba.

Border crossings
Before crossing into Jordan from Israel & the Palestinian Territories, there are a few things you need to remember:
Only change as much money as you need because the commission charged by moneychangers is often ridiculously high
Israeli visas of one month's duration are issued at the Wadi Araba (Rabin) and Sheikh Hussein Bridge crossings, but those issued at the King Hussein Bridge are usually for three months
Jordanian visas cannot be obtained on arrival at the King Hussein Bridge
If you want to visit Israel & the Palestinian Territories, use the King Hussein Bridge crossing and then return to Jordan within 14 days (or three months if you extend your visa in Jordan before leaving), you do not need a second or multiple-entry Jordanian visa
Private vehicles cannot drive across the King Hussein Bridge, but they can be taken across the other borders
On both sides of all three borders there are moneychanging facilities, places to eat and drink, and duty-free shops. On the Jordanian side of all three borders there is a post office and a tourist information counter (8am-2pm, closed Fri).
You can expect borders to be closed on the Jewish holiday of Yom Kippur and the Islamic holiday of Eid al-Fitr.
King hussein (jisr al-malek hussein)/allenby bridge
Only 40km from Amman and 30km from Jerusalem, this border crossing (8am-6pm Sun-Thu, 8am-12pm Fri & Sat) offers travellers the most direct route between the two cities. It is a common way to exit, but not enter, Jordan, because Jordanian visas are not issued at this border - so get a Jordanian visa at an embassy/consulate beforehand, or use another border crossing.
Public transport in Israel & the Palestinian Territories doesn't run during the Jewish Shabbat between sunset Friday and sunset Saturday. On Friday and Saturday it's better to arrive before 11am.
Due to the ongoing intifada (uprising) in the Palestinian Territories, no Jordanian buses were crossing King Hussein Bridge at the time of research. Instead, service taxis run throughout the day from Amman's Abdali bus station to (but not across) King Hussein Bridge (JD2.500, 45 minutes) or there's a single daily JETT bus (JD6.500) at 6.30am. These services may move to the Wahadat station in the future, so check with your hotel.
The ride to the Israeli & Palestinian Territories side, although extremely short, can seem to last an eternity with repeated stops for passport and bag checks. At the time of research, it was not possible to walk, hitch or take a private car across. Buses (JD2) shuttle between the two borders. There are moneychanging facilities on your way to the exit.
The historic oddity of this crossing has remained enshrined in the fact that, on leaving Jordan, you're not really considered to be leaving Jordan. Prior to 1988, Jordan laid claim to the West Bank as its own territory, and somehow this idea has remained in the approach to visas. If you wish to return to Jordan from the Palestinian Territories on your current Jordanian visa, you need only keep the stamped exit slip and present it on returning by the same crossing (it won't work at the other crossings). You must return within the validity of your Jordanian visa or its extension.
At the Israeli border post, plead with the officials to stamp your Jordanian exit stamp rather than your passport.
Travelling into Jordan, the Israeli exit tax is a hefty 127 NIS (around US$29; compared to around 70 NIS elsewhere), supposedly because you're paying to leave Israel & the Palestinian Territories. Note that, if you intend to return to Israel, you must keep the entrance form given to you by the Jordanians - they may well insist on you prolonging your stay in Jordan if you cannot present it.
To get to Jerusalem from the border, take a sherut (Israeli shared taxi; around US$40 for the car) to Jerusalem's Damascus Gate. Alternatively take a cheaper bus to Jerusalem or, if that's not running, a bus to Jericho and then a sherut to Damascus Gate. Much of the public transport in the West Bank was not running when we were there.
In all, crossing the border can take up to three hours, depending on Israeli security measures; avoid 11am to 3pm when delays are more common.
Sheikh hussein bridge (jisr sheikh hussein)
The northernmost crossing (Jordan Bridge to the Israelis; 6.30am-10pm Sun-Thu, 8am-8pm Fri & Sat) links northern Jordan with Beit She'an in Galilee (Israel & the Palestinian Territories), 6km away. It's handy if you wish to visit northern Jordan, and it's the closest crossing to Jerusalem and Amman that will issue Jordanian visas on arrival.
From Irbid, regular service taxis leave the West bus station for the border (750 fils, 45 minutes). From the bridge it's a 2km walk (or hitch) to the Israeli side, from where you have to take a taxi to the Beit She'an bus station for onward connections inside Israel & the Palestinian Territories.
If you're coming from Israel & the Palestinian Territories, take a bus to Tiberias, and change at Beit She'an (6km from the border). From there, take another bus to the Israeli border (allow enough time because there is only a handful of buses per day). After passport formalities and paying Israeli exit tax (70 NIS), a compulsory bus takes you to the Jordanian side.
From the Jordanian side, either wait for a minibus or shared taxi to Irbid (from where there are regular connections to Amman), go to Shuneh ash-Shamaliyyeh (North Shuna) by private or service taxi, or walk (3km) to the main road and flag down a minibus or service taxi.

Wadi araba
This handy crossing (formerly Arava, now the Yitzhak Rabin crossing to the Israelis; 6.30am-10pm Sun-Thu, 8am-8pm Fri & Sat) in the south of the country links Aqaba to Eilat. To get there from Aqaba you'll have to take a taxi (JD5). Once at the border you can just walk across. From the border, buses run to central Eilat, only 2km away. All in, Aqaba to Eilat takes about an hour.
If you're travelling from Jerusalem and you want to skip Eilat, ask the driver to let you out at the turn-off for the border, a short walk away. Israel & the Palestinian Territories exit tax is 68 NIS here. On the Jordanian border take a taxi into Aqaba (JD5, 15 minutes) or you could negotiate a taxi fare direct to Petra (around JD25, two hours) or Wadi Rum.

Bus
Several cities in Jordan are now regularly linked to cities in Israel & the Palestinian Territories. Travelling by bus directly between Amman and Tel Aviv will save you the hassle of getting to/from the borders, but it's more expensive than crossing independently, and you'll have to wait for all passengers to clear customs and immigration.
From Amman, Trust International Transport (06 5813427) has buses from its office at 7th Circle to Tel Aviv (JD21, six hours), Haifa (JD18, seven hours) and Nazareth (JD18, seven hours), departing daily except Saturday at 8.30am. Services cross the border at the Sheikh Hussein Bridge. Buses leave from the Trust office in Irbid (02 7251878) at around 10am. Book tickets the day before.

Car & motorcycle
If you're driving from Israel & the Palestinian Territories, use the border crossings at Sheikh Hussein Bridge or Wadi Araba/Rabin (it is not possible to drive over the King Hussein Bridge).

Saudi Arabia
Getting a visa, even a transit visa, to Saudi Arabia is a very difficult feat. for details.
The main land route for public transport into Saudi Arabia is at Al-Umari, which is located along the highway south of Azraq. The other two crossing points are Ad-Durra, located south of Aqaba, and further east at Al- Mudawwara. Several companies run services to Jeddah and Riyadh from Amman's Abdali bus station.

Syria
If you want to travel directly between Damascus and Amman, it's worth taking a direct bus or service taxi. Otherwise you may end up spending more time and money once you catch a service taxi to Der'a, organise your own transport across the border, get another lift to Ramtha, perhaps another to Irbid, and then a connection to Amman. The only reason to travel this way is if you want to stop off en route at places such as Ezra'a and Bosra ash-Sham (Syria), or Jerash and Umm Qais.
If you are headed to Syria from Jordan, make sure you get a Syrian visa before arriving in Jordan, either in your home country or in İstanbul, Ankara or Cairo.
Border crossings
The two border crossings between Syria and Jordan are efficient and relatively painless on both sides. If you intend to drive between Jordan and Syria, the better border to cross is at Der'a/Ramtha.
Der'a/Ramtha and Nasib/Jabir are both open for 24 hours every day. The Jordanian sides both have a post office and tourist office (8am-5pm Sat-Thu, 8am-2pm Fri), moneychangers (open most of the time) where Jordanian dinars and Syrian pounds are changed, and places to eat and drink.

Der'a/ramtha
Ramtha is the border most commonly used by foreigners who are using nondirect public transport and/or detouring to sights in northern Jordan. You can get direct transport between Damascus and Irbid or Amman, without stopping in Ramtha, though there are also buses to Ramtha from Amman's Abdali station (500 fils, two hours) and Irbid (250 fils). From Ramtha, service taxis and minibuses run regularly to the border. If hitching, ask the immigration office on the Jordanian side to flag down a vehicle for a lift to the Syrian border.

Nasib/jabir
Most service taxis between Amman and Damascus now use this crossing. It's also useful if you plan a detour to eastern Jordan (eg Azraq), as the border at Jabir is useful for connections to Zarqa or Mafraq.

Bus
The air-conditioned Jordan Express Travel & Tourism(JETT; 5664146; Al-Malek al-Hussein St, Shmeisani) buses travel between Amman and Damascus (JD5, five hours) twice a day, at 7am and 3pm; book a day in advance. JETT also has a daily bus to Aleppo (JD7.500, eight hours) at 2.30pm. JETT's international terminal is just up from the Abdali bus station in Amman. Afana(4614611), next door, also has an evening bus to Damascus (JD5, five hours), leaving at 9pm, but it arrives very early in the morning and services aren't quite as reliable. Buses drop passengers off at the Baramke garage in Damascus.
The Palace Hotel in Amman has started a useful minibus service which runs between Amman and Damascus, with stops en route at Jerash, Bosra and Shaba (JD25 per person). They require a minimum of four passengers.

Service taxi
The service taxis to Damascus (three hours) are faster than the buses and run at all hours, although you'll have to wait longer in the evening for one to fill up. Service taxis take less time to cross the border than trains or buses because there are fewer passengers to process, and the drivers are experienced in helping passengers with immigration and customs formalities. These taxis are huge, yellow (or white) and American-made.
From Amman, service taxis for Damascus ('ash-Sham' in Arabic) leave from the eastern or lower end of the Abdali bus station; from Damascus, they leave from the Baramke garage. The trip costs JD7 from Amman, and S£500 from Damascus. Service taxis also travel between Damascus and Irbid (South bus station, 2½ hours) in northern Jordan for slightly less.

Train
Services on the Hejaz Railway between Amman and Damascus leave Amman and Damascus on Monday and Thursday at 8am, but very few travellers take this service because it is so much slower than a service taxi (you have to change trains at the border, so figure on at least nine hours to Damascus). Tickets cost JD3 (half-priced for kids under nine). The charming old station is located on King Abdullah I St, approximately 2.5km east of the Raghadan station in Amman.
The ticket office (06 4895413) is officially only open from 7am on the morning of departure, although you may well find someone around at other times. To get to the station, take a service taxi from Raghadan station, or a private taxi (around 800 fils).