The reactivity of free radicals has the potential to cause major problems for the body, as we've just seen. However, on occassion these potent customers can be put to more productive uses, of which there are two main categories.
1. Killing of microorganisms
It is one thing for phagocytes (like neutrophils and macrophages) to ingest a foreign organism, but the problem still remains to kill them. Usually, a cocktail of substances is thrown at the poor swallowed microorganisms. Some of these substances are specific enzymes that targeting a known weak spot in the organism's defences. However, a large portion of the cocktail is simply non-specific reactive oxygen species, which consist of free radicals derived from oxygen. In this way, the damage of free radicals can be unleashed on a foreign body.
Let's look at one specific example in a little more detail. Say a neutrophil phagocytoses a bacterium so that the bacterium is now within the cell imprisoned in a vacuole called a phagosome. Immediately, a particular enzyme grabs hold of oxygen and converts it into a substance with the awesome name of superoxide (O2-). As the formula shows, this compound is a free radical, and it is capable of wreaking the appropriate amount of havoc. On the way to being neutralised by the body (you can't leave it going for long!), it cycles through a number of damaging intermediates, like hydrogen peroxide (H2O2) and hypochlorous acid (HOCl, 'chlorine bleach'), which also contribute to damaging and killing the bacterium.
2. Cellular signalling
The experts are divided on how extensive the role is for free radical cellular signalling. Certainly, nitrous oxide (NO) is both a free radical and is capable of an enormous amount of effects on things like vascular tone, cytokine production, neurotransmission and even penile erections.
Things become a little murkier when we move away from this particular example, though. Free radical damage can certainly induce apoptosis or necrosis, but this is unlikely to be a designed effect of the free radicals. For instance, it makes more sense to view any induced apoptosis as being part of the body's 'disaster management plan' when presented with catastrophically damaged cells.
There are arguments both for and against free radicals being extensively used by the body for signalling purposes, but I don't have the expertise to judge them in the depth they deserve, I'm afraid. Anyway, it should be enough for our purposes to simply have heard of the topic. :)