In an ideal world, all bikes would be:
- durable an
- good to ride
But in the real world, you can have only two out of those three properties. Add the folding factor and you can still pick only two. In other words: cheap folding bikes are both inefficient and shoddy; and whilst you can have a folding or take-apart bike that's great to ride, it will be more expensive and less durable than an equivalent non-folding bike.
Once you've got over this reality check, and saved up a bit more, you'll find folding or take-apart versions of most sorts of bicycle. The most popular sort however, is the commuter folder, of which it has to be said that a British-made Brompton is the premium example.
This sort of bike is designed to fold as quickly and as small as possible for rapid access to and from public transport, with no stowage hassles - although some operators will insist that even a Brompton is put in a bag. With only a few miles to ride at either end of the journey, commuter folders don't have to be particularly efficient or comfortable to still be a whole lot better than walking! Pay enough though, and they can nevertheless be quite good to ride. Some people even tour on Bromptons!
(Left) A folding bike makes travelling by public transport much easier
At the other extreme, you have bikes that are designed primarily for performance that will fold or take apart, but only if they have to. Dismantling may take quite a while and result in a load of bits for which you need a suitcase, but that might not matter when all day or all week is spent riding. Regular steel or Titanium frames built with S&S couplings make the smallest sacrifice to portability.
Between those two extremes lie many more or less portable, less or more fun to ride bikes, from Dahon, Airnimal, Bike Friday, Birdy... to decide what sort of folder you want, read the reviews from back issues of Cycle  magazine listed below.
Note: CTC members must log in first to access the links below or send a SAE to CTC National Office for articles that do not have a link.
Two compact folders  - Brompton and Mezzo compared by Chris Juden - J/J 2011
Touring on a Dahon Cadenza  - by Chris Bell - F/M 2010
'Have bike, will travel - four portable tourers' reviewed by Chris Juden - A/S 2007
'Suitcase sports bikes - Airnimal Chameleon and Bike Friday Air-Glide' reviewed by Chris Juden - A/M 2003
'The Folding Stuff - 5-page buyers' guide' by David Henshaw - F/M 2001