There are various types of folding bikes. Brompton and Birdys fold up small for commuting on trains, and are fine for shorter rides, but are not designed for long day rides.
Airnimal ( 24" wheels) folds up in various ways, not as small, but rides pretty well.
Some bikes are not folding but can be dismantles for transport. The Bike Friday and Moultons all ride well and take down.

Of all these bikes, only the Moulton is highly regarded as a serious touring bike. You can do hostel tours on the others, but not camping.

For touring you can use 700c or 26" ATB wheels (See Thorn bikes at sjscycles.com). You can get S+S couplings to takedown a standard sized frame, but these are not cheap.

If you are looking for a touring bike which can pack down, then the Moulton is best, but take a spare tyre and inner tubes because the wheel size in not common.