I own three gamecubes in different colors also. The only thing you want to watch for is disc read error, the lens can be very sensitive sometimes.
There is a way to fix this problem, but it requires a voltmeter and disassembling your console...
Anyways, the original gamecube that my family bought around launch still works, so I guess they're fairly reliable. Not their most reliable system, but still much better than average.
It's by a long way the most reliable disc based system though.... cartridges don't need moving parts or sensitive lasers so they are naturally more reliable.
My GC had a slight disc-read problem after 6 years.... by slight I mean it would very occassionally crash (I think in total about 20 times in total... most in the last year)
I think I was told it was something to do with the laser (or the plastic casing for the laser) would get slightly warped by the heat from lots of usage. Which meant the laser sometimes had a hard job finding whatever it looks for.
The problems that can occur with the gamecube are nothing compared to problems with the Wii or PS3, which from what i have heard and experienced seem to be close to each other in a kind of joint second.... and both of those are leagues ahead of the 360 or PS2.
Not sure about Dreamcast.
I had 2 dreamcasts go on me, but they were units from gamestop so who knows where they got those from.