What is the best way to get around the archipelago?
The best value option for long distance transport is the train lines. These are comfortable, reliable and efficient. They also have the bonus of avoiding traffic (which lengthens bus journeys by about a couple of hours), meaning that they stick to their timetable. There are 3 different classes of travel available so the price is also flexible to your budget. Unfortunately, the areas which are serviced by train are fairly limited. Java has the best coverage, with train lines running through the north and south of the island. If you are trying to get from north to south (or vice versa), bus is probably the way to do it.
Public buses are very cheap in Indonesia but are typically quite slow. They will make countless stops to pick up other passengers and are obviously affected by the prolific traffic jams in the country. They can often be extremely cramped and rather bumpy. However, they can be quite an enjoyable experience for shorter trips as your companions will doubtless include not only people but also assorted livestock accompanied by be locals who rarely see tourists and will be fascinated by you. For long distance journeys not served by train, it is probably worth paying the extra money to get an overnight luxury bus. These run between the majority of popular destinations (Jakarta, Yogyakarta, Denpasar etc.) and are very comfortable. There is more leg room, the seats recline, and you get blankets and food and drink included in the price. A 14hour journey on one of these buses will cost a relatively expensive 120,000 Rp, but it does mean you get a good nights sleep.
There are plenty of private transport companies which are often used by visitors, but these are generally by far the worst option for getting about. They are around the same price as the public buses, but often operate cramped, uncomfortable minibuses and suicidal drivers. This is especially the cases of the companies located in very touristy areas as they don't need to rely on return business.
If your budget will allow it, internal flights are another option for getting around the country. Indonesia is served by a fairly comprehensive internal flight network flown by a number of local companies. These are more expensive still, but are the quickest way to get around. A flight from Yogyakarta to Denpasar for example, will cost around 480,000 Rp (compared to a luxury overnight bus at 120,000). It is normally possible to book on the day (if not day before) of travel and still get a seat.
How easy/safe is it to rent a motorbike or car?
For most people, hiring a car and driving yourself about in Java would be little short of a nightmare. The traffic is very bad, roads are poorly signed and some of the driving standards exhibited are questionable to say the least. Hiring a car with a driver or using taxis tends to be a much better idea.
In Bali and Lombok, hiring a car can be a good and relatively cheap way of getting about. Hiring a car with a driver/guide is marginally more expensive, but is perhaps a better idea as it will mean avoiding all the problems associated with driving yourself about. Avis, Hertz and other international car hire agencies are well represented, but there are also many local companies about. The local companies are always cheaper, but have the disadvantage that the cars may not be properly insured (even if they tell you otherwise). Your insurance from home might not cover being involved in an accident from renting a car/motorbike, so it's worth checking that before you leave.
One way rental is a possibility with bigger companies but expect it to cost a lot more. It's a good idea to always fill up the tank before you bring the car back too, as petrol is cheap and the fee you would otherwise be charged is expensive.
You are almost always asked to leave your passport as a deposit for any vehicle that you want to rent, but there is obviously a risk in doing this. If you negotiate, some places will let you leave travellers cheques or cash instead (local hire firms are generally more flexible than international ones). Bear in mind that if you have any sort of problem and have left your passport, you will be in a very weak position when it comes to negotiating how much the damage costs. Your embassy and/or the police may be able to help you, but don't count on it.
Check a vehicle thoroughly before hiring it as they are not always in pristine condition, particularly the cheaper ones. Point out any existing damage or scratches before you hire, or don't be surprised when they try to charge you for them later.
Most of the roads and highways are in good condition, and have two or three lanes on each side. Passing on blind corners is not uncommon. Buy a decent road map before you set off, and don't forget that Indonesians drive on the left! Driving at night is not a good idea, as it can be impossible to find your way on the not too well signposted roads.
Hiring a motorbike is also possible, but even more risky than hiring a car. If you are not an experienced rider, Indonesia is not the place to learn. Highways are busy, fast paced and driving conditions extremely unpredictable. This goes double around the Yogyakarta area where accidents are very common (the Yogyakarta-Solo highway is the most dangerous road in Indonesia). Most towns and islands have good local transport, which is cheap and abundant. This may be a better option than involving yourself with the stress and dangers of driving.
If you have to misfortune to get into an accident, as a foreigner it's likely to be judged as your fault (even if it wasn't) and you will be expected to pay for any damage caused (to vehicles and people) there and then. If someone is injured, the asking amount will be increased to cover the treatment costs - these amounts are definitely up for negotiation, strange as it may seem. Any serious injuries and deaths will definitely involve the police being called - you may still be able to get out of trouble by paying enough money, but it's not certain.
If you plan on driving in Indonesia, bring both an international driving license and your home driving license. You won't (usually) be asked for either of them by the renting companies, but having both will likely be a great help should you happen to get into any legal difficulties.
Is it safe to take luggage on an overnight bus/train?
Theft is fairly rare on overnight transport. When travelling by train, all luggage will be inside the carriage with you, probably within your sight. On overnight buses luggage is locked in compartments underneath the seating areas so no-one can get to luggage during the journey. On buses, be aware that thieves have been known to take the seat behind you, cut your bag and take your belongings before you realise it. This sort of theft is most common on local day buses, but it does happen on more upmarket transport too. Keep an eye on your belongings and you should be fine.
Do I need to make bus/train reservations before I travel?
For the long-distance buses, you can turn up at the bus station at pretty much any time. Chances are that the bus you want will be leaving within half an hour, and will have free seats. Same day reservations are often obtainable for trains, but during busier tourist periods (July and August) you may need to book a couple of days in advance. Train reservations can be made directly at the station; some travel agents also offer this service.
What are the boats to the Islands like?
If travelling to large islands like Bali, a number of large ferry services operate to other islands in the vicinity. If you go to some of the smaller islands (e.g. The Gili islands off northern Lombok), boats are much smaller and a bit rickety. In good weather they are fine, but in rough weather the ride can be a bit turbulent. Some of the islands further off the main land are inaccessible at some times of the year due to storms. Ask locally before attempting to travel.
How safe are Indonesian domestic flights?
Safety on Indonesian domestic flights obviously cannot compare to large international operators, but generally is still pretty good. Garuda Indonesia's (who run the majority of internal flights) safety record is comparable to other operators in the region, with only a handful of accidents in the past 30 years. You may often feel safer flying in order to avoid the questionable driving standards on much of Indonesia's roads!