@ mehtaatur - The things I know that can control high amperage devices are mechanical relays, solid state relays, and triacs. I've never worked with SSRs or triacs but relays are easy to do with an Arduino; there's at least one example here on arduino.cc.
The thing about relays is, they scare me. Actually they don't scare me as much as the thought of making just one small mistake or miswiring or something I overlooked or didn't know about in design, and having my house burn down. I'd probably trust myself with a relay controlling something like a sprinkler system or lamp that's only on when I'm in front of it, but if I was going to use it to control an unattended heater or ceiling light I'd probably get something like:
so I'd have someone to sue if things go wrong...
Regarding wireless -- I've worked with, and like, the Async Labs WiShield for WiFi, but they stopped selling it last March. SparkFun sells one that some people like and some people complain about; I've never used it so I can't comment. The "official" Arduino WiFi shield was announced last fall but hasn't actually started shipping yet; if you look around the forum you'll see plenty of people (myself included) are anxiously awaiting it's release.
@ AndrewStone - Thanks for the laugh.