Your question asks if the resume needs to include this, and I think that it does not -- so yes, it's ok to omit it there. However, as others have said, it's rude to start down the application path without disclosing information that a company might consider to be a deal-breaker. So you have to tell them, but you don't necessarily need to do it on the resume if you don't want to for some reason.
This is where the cover letter comes in. In the cover letter, after your pitch, you say something like "I currently live in $location and am open to relocation". If you do not need relocation assistance for some reason, say so -- you've just gotten less expensive. (Maybe you're going to be moving to the target location anyway, for instance. Maybe your spouse already has a new job there with relocation.)
Further, for all but the smallest companies, there is likely to be a formal application that you have to fill out. This will ask for your current address, among other things.
If you are are only concerned about being rejected by the initial HR screener, then this really doesn't make a difference -- do what I advised or just put it on the resume. But if you fear that your location might influence other reviewers (e.g. because of prejudices), you can do what I've suggested and leave it off of the resume. The resume will be passed around; the cover letter might not be and the application generally won't be (at least in my experience). When I (technical person, not HR) am given a resume to review I don't care about where the candidate is coming from (not my problem), only what he can do, and I've reviewed resumes that only included an email address without blinking. My own resume does not include a physical location and this doesn't appear to be hindering me (though I am not open to relocation, and say so if applying to a company with locations outside my own city).
