Another common issue which I've experienced several times on a few people's PCs is the fan sticking in the power supply. This causes it to overheat and start giving off a burnt rubber like smell once the PC has been running for a while. The simplest way to check this is to put your hand at the back of the PSU and feel if there is any air blowing out. The power supply should also not be hot to the touch either.
Like Alan mentioned, the graphics card fan is another that can get clogged with dust and stick over time and is something that has happened with my previous graphics card.
Finally, it's worth doing a visual inspection of the fans inside the PC by removing the side panel and power up the PC to make sure all the fans spin (rear fan, CPU fan, graphics card fan and chipset fan, if present).
Basically, if the smell is like burnt plastic or rubber, you should start investigating it before something more serious happens.