PS2 and Xbox have more problems then the GC, but its not in anyway gauranteed to do so.
I know many people that have had their PS2 go bust on them, I know very few people that have had their Xbox do so.
But:
The xbox has a hard drive, and ALL mechanical things will eventually fail because they use motors, moving parts, etc.
This goes for all consoles, but it depends on how heavy a user you are of your consoles. How many hours/year do you end up playing them really? I really doubt your GC will ever die, it will probably easily last 7 years or more is my guess. I have PC CDROM drives that are over 8 years old still kicking and they see constant use.
Buying used should be no problem as long as the user of the used console didn't abuse it (drop it, leave it on 24/7 365 days a year, etc).