How many amps do a standard Core 2 based computer (assume ATX form factor with fans and a decent graphics card) require? Can a system be safely run on a 20 amp breaker?
Yes, it definitely should.
Most consumer electronics are specifically designed and rated for use in homes which in North America use standard outlet, fuses, and breakers of 15A. If a computer system (or television or whatever) were to require too much, it would not be certified for use in homes.
If you happen to overload a system (with a dozen drives, multiple video-cards and monitors, dozens of peripherals, etc.) and are curious, you can get a meter like the Kill-a-Watt, plug your stuff in to a power bar, and plug that into the meter. Then you can monitor all kinds of information about the power usage (especially the most relevant ones: Watts/KWH). You don’t even have to buy the meter; check if your local library has one for loan.
Well, i've run 2 c2d systems, a CRT and an LCD monitor on the standard 13 amp power plug attached to a multiple socket in my apartment, so it should work.
Doing the math - your voltage is fixed, and lets assume that the power rating of the PSU reflects the maximum power needs you have - P = IV.
Even at maximum load, assuming a 110V supply voltage, and say, a 1kw power supply (overkill for most cases), the system won't draw more than about 10 amps at maximum power use. More typically you should be seeing much lower power use and current draws, maybe 5 amps or less - say up to 5A for a 500W PSU.
The 17 inch CRT i have as a spare has a 2A rated current draw (according to the back back) at 220V - it would presumably be twice that for the same amount of power at 100, so lets assume 2-4A (assuming i haven't totally misunderstood power draw with respect to power voltage.).
You should be able to run it safely with no issue