This question depends a lot on what your objective is. If you just want your monitor to look pleasing, playing around with the monitor controls will probably get you where you want to go. If your objective is to have your screen closely match what you will get back from a professional color lab, things get a bit more sticky!
Most monitors can't get the latter right, with or without calibration. A few years back you could get a Sony Trinitron (or rebranded as DELL, Gateway, etc.) And you could calibrate those for precise color work. After those were discontinued a few years back, I picked up a few used ones and they looked perfect. But when I ran a calibrator on them, it was clear that one of the guns was "getting tired" at the bright end of the range. That meant a tint shift that couldn't be corrected properly.
Unfortunately, most consumer LCD screens can't match those old Trinitrons. That's why pro photographers are spending 100s to 1,000s of dollars on high quality monitors. I bought a NEC monitor for about $800 a year or two back and I consider it "adequate." But that is really at the low end. Hopefully when I need a replacement, there will be newer monitors available that are better and perhaps cheaper.
There are tons of info out there about choosing a proper monitor and calibrating it successfully. For most home uses though, doing an eyeball calibration using the monitor controls will probably be satisfactory.
