Lots of good advice, but as a former house painter (high school and college years), I agree that free-hand "cutting in" is best, quickest, and easiest overall. It takes practice, but once you get it you'll never waste time with tape again. Make sure you use a very high-quality brush (Purdy brand are what I always use), and get a 1" to 1 1/2" angled brush that's made for the type of paint you'll use. Never skimp on brushes, because you get what you pay for. More expensive brushes are thicker and more consistent, which allows for more precise control. Also, FYI, if you're going to spend a lot on brushes, get a "spinner" (a plunger with a holder for the brush grip, used to spin the brush dry after cleaning cycles). Use the brush to paint all the areas of the wall that you can't get with a roller (corners, baseboard, by ceiling, around outlets, etc.). Then roll, going as far into the previously painted areas as possible to create as consistent a surface as possible.
If you must use tape, as others have said, take it off as soon as possible, and do not let much (any) drying occur. Unless you used excessive amounts of paint just above the tape, you'll have no problems with drips by taking the tape off before the paint's dry (just make sure the tape doesn't touch the wet wall as you remove it).
Two things are infinite: the universe and human stupidity. And I'm not sure about the universe. -- Albert Einstein