To give you a personal example, I've been using a Canon 30D for about 8 years and it now has an estimated shutter count well over 100 000 (I haven't been keeping perfect track, but I have somewhere around 250 000 images stored with a large number of them being from that camera body). I also have a Canon 5D Mk1 with around 100 000 shutter actuations. The 30D did need the mirror mechanism replaced around 80 000 shutter actuations and that cost about $200 to fix. Neither camera has ever "worn out" or "broken" per se, but they have needed minor repairs from serious use.
(I should point out that with a "point and shoot" camera, when something fails, they are more or less disposable and should probably be replaced rather than repaired)
I am in need of a new camera, but it's because I work with low lighting a lot and need a camera that works better in difficult lighting situations. Nothing to do with age, only with technology.
At this point, lenses also need repairs - sometimes a diaphragm will wear and need replacing too.
For average hobby photographers, the chances of taking hundreds of thousands of images with a DSLR are slim; anything over 8 megapixels will produce beautiful prints and should last as long as you want to keep it.