Q:

What should I look for in an indoor cycle trainer?

I'm considering getting an  indoor cycle trainer . I had a look on ebay. There are a lot, and the price ranges from under 20 pounds to several hundred pounds. Quality and function range accordingly, so I'm a bit lost.
My main reason for getting it is to use it for cardio fitness training. So, I'm looking for something that meets these criteria

a) Its got to be stable (no annoying rocking / wobbling)
b) As small/compact as possible so it can be packed away (while meeting criteria a)
c) I can change the resistance, or incline to increase the cardio workout. Preferably mid workout. 

Can anyone recommend a trainer that meets these requirements?

A:

I can't recommend any specifics offhand, other than I've used two different types of Tacx trainers and have been very happy with them. Both were in the $150-$200 range new.
A couple of comments though:
a & b: Virtually any trainer on the market is going to be pretty stable unless you are out of the saddle and sprinting. As long as it's not a really low end one if you are wobbling you might want to spend some time working on spinning smoothly. And most everything on the market will fold up a bit, though not tiny. Think something in the loose ballpark of the size of half a wheel.
c. If you're looking lower on the budget range, don't worry about not being able to switch the resistance mid-workout on the trainer. You can get a wide range of workout just by shifting gears on your bike. 
d. (you didn't mention this one) Noise level. Some of the wind and magnetic trainers are loud. If you can try it out, great. The tacx trainers I've used were relatively quiet. The Minoura one I've used was painful.

A:

My only cycle trainer experience is with the one I bought, an Elite Fluid Primo.  It's a fluid trainer with a beefy stand, so less noisy than other types and the design is fairly simple.  Just a matter of clamping the trainer onto the bike's rear axle and you're ready to go.  As an apartment-dweller, I've got the whole thing setup on rubber tiles from Home Depot to reduce the amount of vibration sent to the neighbours below.
As far as your criteria:

Stability is great, despite my initial skepticism.  At 225lbs I can get out of the saddle no problem although it feels odd not balancing the bike yourself.
Folds down to about 8" tall, 26" x 18" so not too difficult to store.
Resistance is based on how fast the wheel spins:  gear up for more, down for less.

As geoffc points out, riding a trainer indoors gets very hot.  I set mine up by the balcony door and only use it in the winter so that I can get plenty of cool air.  It's also pretty mind-numbing to ride, after an hour I've had enough.  I only use it in the off-season and combine it with a heart rate monitor to decide how hard to push.

A:

I cannot recommend a specific model, there are way too many products.  I have a Cyclops Fluid trainer that is ok.  I hate riding a trainer, it is too dang hot indoors for me.  
The tripod stands most trainers use look less stable than you would imagine, but they really can be quite stable.  
With a fluid trainer, the harder you ride, the harder the resistance.  So actually spinning fast is pretty hard to do on it.  
Most of the tripod style ones, the support legs fold back to the frame, so it is as thick as the resistance mechanism is thick.  
I would NOT get a wind trainer!  Even the fluid trainer I have is louder than I would like, but the other options are louder.  

