For instance, I just fixed a 2c plastic clip that pretty much made my microwave unusable by virtue of the door being un-openable. In order to do so, I had to have my fingers about 3 inches away from a bare wire transformer which near totally obstructs what should be a very simple fix.
Plenty scary and dangerous enough for me to have to call the manufacturer and find a certified local repairer...
Friend had an older washer with a giant "timer dial" that was cheap to fix - the new dial cost like $50 and was simple to replace. A similar washer that I had had a single plastic part that held the dial in place break, and the only way to fix it was either bolt some metal strapping around it (which I did) or buy a new faceplate at $350 (+ shipping) - that's half the cost of a SpeedQueen (which I eventually bought when the pump crapped out. The SpeedQueens don't change year to year and they're basically laundromat machines so they're very repairable.
If you do decide to replace an appliance, there are people that will take away the old one for free, because they will repair and resell if possible.