I can run every light, TV, computer, refrigerator, etc, in my house with my 3500W (15A 240V) gen. It can also run our microwave, coffee pot and garage doors, although I've always been careful not to do any of these simultanously. I can even run our range, though the lights blink every time the heating element kicks on. I think it *might* handle one of the 3 ton heat pumps, but I haven't been desperate enough to try it out yet. I'm just happy to have lights and all.
That said, you have to be careful of the small cheap generators; they're not regulated very well, and can put out excessive voltages if they're sized too large/loaded too lightly. The first time I used mine, I had to run around and turn on every light in the house to load mine down to 125V. Fully loaded (like when my stove is on), it's down to 110V. It's a common problem.