I found this:
Apparently, the specs on this device are (from the link above, in case it goes away):
Hamlin Solid State Relays Model# 7178
3-18VDC Control, 24-240VAC 3A Output
So you can control AC devices, as long as they run on 24-240 volts (AC), and only consume 3 amps. Small lamps and other small appliances should be OK, but check their specs first.
Also, Stuart Faust, if you don't have any experience with AC mains current, I strongly suggest you do some more reading on the subject, and perhaps get some help locally from someone you know who does have experience. AC mains is not something you simply "play around with".
Furthermore, you should take precautions to keep your wiring to the SSR as neat as possible. These SSRs are meant to be put on a PCB, so you should keep that in mind, and also keep in mind to keep the low voltage side of things (the Arduino control pins and wires to the SSR) as isolated from the AC mains side of things as possible. If you directly solder wires to the SSR terminals (not really recommended, but doable), make sure you put heat shrink tubing or some other coating (liquid tape or similar) over the terminals to prevent shorts or possible shock hazards. It is better, though, to put the SSR on a PCB with screw terminals on opposite sides of the board, soldering all junctions.