Question: I put that painters tape on the edges by the ceiling and cut in next to it (overlapping the tape with the paint somewhat).

A couple of hours later, I pull the tape, and small sections of paint come off with it. How do I avoid this?

Is it sufficient to just take a small brush afterward and touch up the area? It always seems to look crappier.

Answer: 
Mistakes are bound to happen, and yes you can touch it up with a very small crafting paintbursh (like the ones kids use for waterpainting). You will probably never notice. 

The best solution however, is to not use painters tape on corners and ceilings. Typically in professional painting, tape is not used. If you use a small 2" cutting paintbrush, and apply by pulling the paintbursh at an angle toward you, keeping the smallest amount of bristles near the corner / edge, you will be fine. The only time i apply painters tape is around trim - and this is more to prevent drippings and splatter, than to protect a clean edge.

If you get paint on the opposite wall using this tapeless method, it is most easily corrected by fixing it immediately when the pain it still wet. Simple use a all-in-one paint tool (or a putty knife) with a damp cloth (i use old t-shirts) pulled tight over the edge, then scrape away the paint that got on the opposing wall.
For removing tape without damaging the finish it is stuck to, I've found that if I pull the tape back over itself and run my hand parallel to the surface I get the best results. When removing tape, the natural tendency is to pull it perpendicular to the surface which puts the most stress on the underlying paint.

As already mentioned, most pros don't use tape. This may sound more difficult, but with a little practice it's not hard to master. It's also going to save you time. The Purdy paintbrush company has an excellent set of instructional videos with tips on how to cut in by hand. If you search for ["purdy cutting in"](http://www.google.com/#&q=purdy%20cutting%20in) you should find links to short little videos on the Purdy site as well as on YouTube.

One other tip that I learned from my painter is to caulk the corner between the ceiling and the walls to help get a nice crisp line. Depending on what type of texture is on the wall this can really help.