A UPS can be a huge lifesaver, my little APC has saved my data life more than once. I like the APC's so well that I have a little unit on every office computer, and a big APC on my warehouse computer so that the staff can continue printing pull tickets and shipping invoices if we loose commercial power for several hours.
A couple added points:
First, make sure that you run ALL power cables, ethernet, cable, telehone and anything with a USB connection to the CPU powered through the surge protection of the UPS. Everything needs to be ran through the unit, no exceptions. That does not mean everything needs to have battery backup, just that the power source is filtered and protected by the UPS.
Secondly a single point of surge protection is better than seperate points of surge protection for each downstream unit. The reasoning is that the amount of surge protection on a given surge protector unit is proportional to number of outlets and the rated value of the items typically installed on the protector. The modern UPS is capable of having a large number of items installed and is known to be routinely handling high value CPU's and expensive monitors, thus the surge protection rating is usually quite large and often far in excess of actual need. The small, off the shelf stand alone surge protectors, especially those discount department store 4-6 outlet surge protectors, usually are quite small relative to the surge protection value and even several of those small surge protectors combined together will not have the same combined surge protection value as a small UPS.
Thirdly, if you were to plug your ethernet and router (as an example) into a small surge protection unit, and then plug the ethernet into the UPS and a major surge were to happen, the insurance companies for the various surge protection units will get into fight as to which company's unit failed to stop the surge. A single surge protector eliminates the potential fighting and denial of claims.
And last but not least, chasing Ghosts is what my technical people do for a daily wage. Having several items operating in a complex system with accessories being powered through seperate outlets (and surge protection units) can cause electrical noise and interference problems. The source of the problem is that the items are no longer sharing a single electrical outlet. Yes most surge protection units have a noise filter installed, but sometimes it is not adaquate. My techs have chased many a Ghost that was ultimately discovered to be related to seperate outlets being used for a complex system with seperate outlets for accessorial items, with the usual culprit being a decaying ground for one of the outlets. A decaying ground may not as large of an issue for a system operated from a single outlet as the entire system will be operating from the same ground value.