Saudi Arabia has 4 international airports in Riyadh, Jeddah, Madinah and Dammam. The airport in Dhahran is now closed to civilian traffic, so passengers to the eastern region now fly to Dammam or nearby Bahrain (which is much better connected) and then drive to Saudi Arabia.
Saudi Arabia is served by the national carrier Saudi Arabian Airlines, which has recently been rebranded to its Arabic name Saudia. Saudia has a reasonable safety record, but many of its aircraft are outdated and the quality of service, in-flight entertainment, etc. tends to be low. Virtually all Gulf airlines and most major European airlines fly to Saudi Arabia.
During the Hajj, numerous charter flights supplement the scheduled airlines. Foreigners living in Saudi Arabia can often get sensational discounts on outbound flights during Hajj. Airlines from Muslim countries fly in many loads of pilgrims and do not want to fly back empty.
SAPTCO operates cross-border bus services to most of Saudi Arabia’s neighbouring countries and even beyond, e.g. to Cairo.
Probably the most popular connection is between Dammam/Khobar and Bahrain, operated by the separate Saudi-Bahraini Transport Company (SABTCO). There are five daily connections at a fare of SAR 50/BHD5 and the journey across the King Fahd Causeway takes about two hours on a good day.
There are car crossings at almost all borders, although those into Iraq are currently closed. The eastern crossings to Bahrain, Qatar and the UAE are heavily used, all others rather less so. There is currently no land border crossing with Oman; it is planned to open the first such crossing by the end of 2012.
There are no railway lines connecting Saudi Arabia with other countries, although in the north one can still find parts of the Hejaz railway, which once led to Damascus.
Rare passenger ferries run once a week or less from Egypt and Sudan to ports in western Saudi Arabia. (Service to Eritrea has been discontinued.) Slow, uncomfortable and not particularly cheap, these are of interest mainly if you absolutely must get your car across. An unofficial ban on Western travellers may still apply.