I generally use plugin surge protectors as power bars, since my household wiring isn't amenable to putting in a clean installation. In some places I've got a couple of surge protector/power strips running off of a surge protector/power strip.
Your computer and every device that connects to it that uses AC power should be connected through a surge protector of some sort to prevent voltage transients when the lightening hits the power pole (common in my area), or when the truck knocks one pole into another (common in some areas), or just when the air conditioner and/or refrigerator kick on/off etc. Ideally, everything would connect from the same surge-protected "power bar" so that everything grounds to the same point.
If you're on a dial-up connection, the telephone wire should run through a similar device, and many of the economical "extension cord" type surge devices have in-and-out phone jacks for doing that. Voltage transients that won't harm your telephone can destroy the modem in your computer. (In fact, a couple of the built-in modems have been our only "surge loss" in the past several years, even with protectors on the lines; but that was a pretty horrendous lightning storm-event.)