I keep my resume and linkedIn up-to-date, and my boss knows that occasionally opportunities and interest pop up. However, he's a very understanding guy and he encourages people to see what's out there.
I think it's always a good idea to periodically look at the job market, see what's in demand, and make sure you're still marketable. You don't want to let your skill set get stale. i see it as equal to reading industry blogs or magazines. You need to be up-to-date with what's going on in your field.
It used to be I would get calls from recruiters almost ever day, but now that the economy has taken such a hit it's much less frequent. However, beware of recruiters. A lot of them are trying to fill contract or temporary positions, or contract-to-hire jobs, which means that stability can be an issue, and recruiters lie. A lot. Don't find this out the hard way.
Generally when a recruiter calls, I tell them that I already have a steady full-time gig and that I'm not able to do contract or contract-to-hire work. Some of them understand, others don't want to take "no" for an answer, at which point your best bet is to tell them that you're not in the job market right now.
The pitfalls are that your current employer may take it personally that you were looking at other jobs, or see it as a sign of disloyalty. this makes you slightly more vulnerable to layoffs, firing, or a change in the way your employer treats you. However, if they're good and they value you, they may be willing to make a counteroffer and/or match the amount of the new job offer. It really depends on your relationship with the current employer.
Also, if you're thinking it may be a good idea to look around, stop and ask yourself why. What is it that's making you want to look around? Is it something that can be remedied? Are you just ready to try something new? This is all important stuff to think about, because it may be better to just resolve things where you are if its at all possible.