A good baseline rule of thumb (in a welding book I have) for steels is 1 amp per .001 in of thickness. So 1/4" would require 250 amps for a full penetration single pass with no joint bevels. For aluminum, double the required amperage (heat runs away from the weld faster and you can't build up the heat without more amperage).
This rule is a little overkill in practice but I think it is aimed at a 100% duty cycle. Meaning if you want to weld 1/4 non-stop with no breaks for cooling, you would need a 250 amp machine. I think most would agree that the 140 amp 110v machines would not make a full pen closed gap butt weld on 1/4" steel, much less do it continuously.
Shielding gas also plays a role in the heat transfer equation. If you use a less dense gas like helium, more heat will stay in the weld (more common when welding aluminum). If you use a denser gas like CO2, more heat will be transferd from the weld into the gas, thus requiring more amperage to maintain the puddle.
bmc69- Correct me if I'm wrong or not in the ballpark.