The classic Leica is full frame. The camera that started it all by turning 35mm cine film sideways and putting it in a still camera. The film itself is 35mm wide in total, but after the sprocket holes the image height is 24mm, and to create a nice oblong image, it is 36mm long. That is 'full frame 35mm' as distinct from half-frame, which never caught on for reasons of image quality and is pretty rare.
While this might sound like a bit of a bodge, for mainly optical reasons it's a pretty good size. It's adapted itself very well to the SLR camera design and despite numerous attempts to 'improve' on it, they all failed (notably Kodak APS and it's variants).
Then there is medium format, which basically means 120 film. That comes in three main sizes - 6x6cm, 6x4.5cm, and 6x7cm. You can get digital versions of these, but they're all 6x4.5 or a bit smaller, and cost a fortune, eg Hasselblad £25k. Image quality is quite good
Fuji have just introduced a new version of their 6x7cm film rangefinder camera, the GF670. The lens folds away and the whole thing is about the size of a paperback book, which shows that it's not the format that takes up the space. Here
http://www.ephotozine.com/article/Fujifilm-GF670-mediumformat-film-camera-announced-13918 A 'full frame 35mm' digital version of that is quite feasable, with a retracting lens, and I think we might see something along those lines, with a short-ish lens. Maybe.
The mega-compacts we see, bridge cameras, have big zoom ranges because they only have to cover a tiny sensor - the size of your little fingernail. Their lenses might be labelled something amazing like 25-400mm, but that is the 'equivalent' focal length range expressed in full frame terms. The actual focal length is more like 5-80mm, and given the tiny image circle they have to deliver and modest maximum apertues, they can be made quite small.
But when you scale that up to cover the image circle rquired by full frame, you inevitably end up with an absolutely massive lens. Even if it was possible, which currently it isn't.