A number of international airlines fly into Indonesia's main international airports at Jakarta, Denpasar, Medan, and Kupang. Other airports, such as those in Sulawesi, Kalimantan, and Irian Jaya, have flights to the Philippines, Malaysia and Singapore, and Papua New Guinea, respectively.
Garuda Indonesia, the national airline, flies to destinations throughout Asia/Australia, as well as to Europe and North America.
Garuda Indonesia
Should you wish to avoid Garuda, there are a good number of other options for flying to Indonesia, among them: Air Asia, Air France, Cathay Pacific, Continental, Emirates, EVA Air, Gulf Air, Japan Airlines, KLM, Korean Air, Lufthansa, Malaysian, Qantas, SAS, Singapore, Thai and Turkish.
Bear in mind that you have to pay departure taxes at all airports upon leaving the country as well as for domestic flights. If you have the Indonesian nationality and go on a holiday abroad, you will have to pay "Fiskal" which amounts to Rp. 1.000.000,00 (march 2002).
There are no international rail services available to spirit you into Indonesia.
There is an international bus service which runs from Pontianak on the West coast of Kalimantan to Kuching in Malaysia. Travel agencies in either city can sell you the tickets. Never forget to bargain. The other land border, between Irian Jaya and Papua New Guinea, is closed.
Everything from high speed ferries to slow-boats are available to bring you into Indonesia. From Singapore and Malaysia, these can be very comfortable affairs, with fast ferries running from Singapore, Penang, and Malacca, to various Indonesian ports, most notably Medan and Bintan. Immigration facilities are present at most ports. It's best to consult a recent and detailed travel guide for further info.