You can buy puzzle cubes, they're made up of irregular blocks that need to be assembled in a certain way to hold together. The only downside to these is that after you "learn" how to put it together by assembling it a few times, it doesn't do much for you, though I suppose you could up the challenge by assembling it blindfolded.

Field stripping and reassembling guns is a good practical entry to mechanics. Again, after you've done it a few times it doesn't really teach you anything new, but the blindfold trick would work well here too.

Lego robots are another good basic intro into mechanical intelligence. You can graduate from them to DIY robotics kits.