I use a couple of mod square wave inverters.  The fridge runs just fine, and when I was running a freezer it was also OK.  I have a small fan but for some reason it runs very slowly.  Most of my power tools work perfectly well, the only exceptions being those that need more power than the inverter can deliver.  The TV makes a bit of audio buzzing, but I can live with it.  some CFL lights also buzz a little bit, but perhaps I'm only noticing it because I'm in a caravan with the lights 2" above my head?

The only item that absolutely refuses to work is my electric razor, because it's an auto-voltage-sensing type that theoretically can be used anywhere in the world (110-120-220-230VAC).  This is particularly saddening to me, because I really hate shaving with a blade. ;-)

I don't know about some of those cordless tools chargers. Never tried one. Anyway, these are the things that I have run on a MSW inverter (AIMS 800W cont 2000W peak MSW):

*Florescent Lights - I have never noticed a flicker with these, but they do run a bit dimmer than when on Grid power.

*CFLs - Work great.

*Desktop Computers - No problems. No lines on the monitor or anything like that. Make sure the inverter is big enough though, because those bigger monitors (17" and up) seem to use quite a lot of power to start up.

*Laptop computers - No problems.

*DSL Modems/Routers etc - These use those 'wall-wart' plug in adapters, and most work fine. The only problem I had was that the adapter my DSL modem came with would not work with the MSW. As soon as I switched from grid to inverter, it would turn off. I checked the voltage, and instead of 12v I was getting less than 8. Strange. Anyway, I replaced it with one of those really cheap adjustable ones from the local electronics store, and it works fine on the inverter now.

*27" TV - works fine. No lines or buzz or anything under normal use. However, when I started to heavily load the inverter, to almost full, and the input voltage dropped to around 11v, black lines started running down the screen. Turned it off after that. Anyway, found that the cables I was using to connect the inverter to the battery were too small, so the voltage was only about 10.5v at the terminals on the inverter! So, replaced the cables with bigger ones and it works fine now.

*Household Fans - Worked fine. Made a bit more noise and ran a bit slower, but didn't overheat or anything.

*Handheld drill - No problems at all.

*Stereo equipment - Hardly any buzz. Not noticeable once any music was playing.

*Fax machine - I have a relatively old (10 years) Canon fax machine, and when plugged into the inverter, it makes a buzzing sound, which was not coming from the speakers. It worked ok, but I felt uneasy about the buzz, so I decided I could do without it when the grid went down.

*Cordless phone - no problems.

I am hoping to be able to run my fridge of the inverter, but I haven't tried it yet. From what people say here though, it should work.