Sandman:
All of the advice above is worthwhile. The reality is that the best method for a particular bike depends on the characteristics of the original paint and the characteristics of the secondary paint. I've had some good results with acetone. In any case, the best idea is to try out the removal method on a small area of the bike that you don't usually see.
Rivnut has a good thought about the likelihood of lead in old house paint. The primary hazard in that case is dry sanding of the paint and breathing of the dust. Naturally, when using a solvent or caustic (e.g., oven cleaner), we should wear gloves (nitrile, vinyl, or latex, as appropriate). Also, paint residue left when a solvent evaporates should be handled with care so as to not create dust.
Have fun!