Some can upgrade processor (generally BIOS dependent, but say if you have an X2 3800+ AM2, then you could 99.99% use a 5000+ AM2 or like an E6300 -> E6700)
Most can upgrade a video card unless it's one of those tiny tiny computers
Just depends, make sure you find out the Expansion Slot info before you purchase, that'll tell you upgradability
Generally, if you get a computer specifically that is built specifically for gaming, it's very upgradable. However, it's good to do a little research before buying a specific brand. I was thinking about buying an XPS system but found out the case for it only accept BTX motherboards - there aren't any BTX motherboards to out there to buy freely. However, everything else looked fine. Also, most manufactuers will not support your computer if you upgrade the motherboard - everything else is generally free to upgrade.
Honestly, with the exception of Dell, most custom builders use retail components;especially in desktops. These are systems you could build yourself with the proper know-how.......so there isnt one part you couldnt replace or upgrade.
That being said, you have to know what parts are compatable with the existing machine.
A little homework is all you need.
Small form factors are generally less upgradable.
Dells are hard because they use proprietary components alot, especially MBs.
I just finnished upgrading my Hp, had a P4ht and some crappy mb, now specs are in sig. Of course the original recovery disks dont work for me anymore but thats fine.