Well, unless you're getting hit by lightning or suchlike, your computer's fragile electrical components are pretty much protected by your power supply (it's a box inside the 'puter). But you don't want your power supply to have to deal with that because first of all it'll have to kill itself by blowing its fuse if the surges go too high (or long), and even if it doesn't short the surges will wear it out very quickly ........dying power supplies cause some of the most difficult to diagnose problems that exist with computers.
A surge suppressor is an extension cord that does its best to equalize power spikes or flip a switch to cut its outgoing power if need be (beware of crappy ones though--I'd say get one with 600 joules or more).
What I'd recommend for you though is a UPS, which serves as both a surge suppressor & a battery, so your computer can ignore those brown-outs altogether.
You can easily get surge suppressors & suchlike which have a connection for dial-up modems (which can fry the rest of your computer if hit by a power spike), so I imagine you can find one with a connection for your cable modem as well, although I've never seen one like that meself.