Hi there,
me and partner both have the following Raleigh folding bike, courtesy of IKEA:
[go to ebay.co.uk - search for 'IKEA BIKE' - you will see them there, I cannot post the link as thorntree wont let me....]
We're going to France, then Spain, Italy, Austria, Germany.
It'll be £120 to take the bikes on 3 one-way flights we're doing, but I presume if we fold the bikes and put them in the small bags they will be free to take on trains? We will camp outside sometimes, and we figured these bikes will be much quicker than walking.
Is it viable to use them most days when a short train journey may not be as useful for seeing about the countries? I don't mind paying £120 in total to take the bikes and get them back to Britain again if it's going to be worth it.
Obvious precautions are bicycle pump, puncture repair kit..... We got the bikes for free, and free bags for each, so if worst comes to worst I guess we could try sell them somewhere at minimal expensive to the buyer.
Any advice for cycling about (including travel insurance!) is greatly appreciated; we want to camp in the countryside in the countries sometimes to save money, and I feel a bicycle is a good way. Folding bikes aren't always hugely comfortable, but we are willing to accept this tradeoff in exchange for a quicker ride than walking between cities, etc.
Thanks,
Graeme.

Folding bikes are great for exploring if you are mainly travelling by train. Once they are covered by a bag, I don't think you'll have any problems with having to pay for them.
Your main problem will be with your bags when you want to cycle, folders aren't very good at load carrying. Perhaps you might try out a trailer? (but note that some folding bikes aren't suitable as the lateral forces are too great). Carrying everything on a backpack while cycling around won't be too much fun (although no worse than walking around with backpacks). Some folding bikes have purpose built trailers available - you can use them for carrying the bike around, then you can put your luggage into them and tow them when cycling.
Other than that, i don't see any big problem for you - standard travel insurance should cover you when cycling, its only if you are mountain biking, etc, that you might need special insurance.
Check things like wheel size, etc., many folding bikes use non standard tyres, inners, etc., so make sure you aren't stranded somewhere just because a tyre blows out.

In that case Philip, there wil be no problem... if you follow my procedure for finding the bike on ebay, you can see there's an Avenir bag, which folds into a pretty small package!
We have booked the folding bikes on with Ryanair. Tip: avoid using their 0905 premium-rate expensive number to add 'winter-sports including bikes' onto your plane journey, simpy phone the national rate (~10pence per minute) number, choose the option for 'adding wheelchair', give the person the confirmation number, ask them if they can ask their manager about a folding bike, thus distracting them, then get the cover added without the £5 call.
We've got 65l litre eurohike rucksacks, and will use cable for attaching the bags to the back of the folding bikes. If you go to ebay you can see a picture of the bikes, they include a 'holdy-baggy' thing at the back, thankfully.
Almost organised for the trip now, should be great!