From what I've read, the advserse events associated with infant Tylenol or Ibuprofen (either immediate or later in life) are almost all related to A) overdoses, B) long-term use, C) drug interactions when babies are taking numerous other drugs, D) allergic reaction to their ingredients, E) pediatric patients who already have hepatic or renal failure or diseases. There is no evidence that an appropriate dose here and there for teething pain is going to harm a healthy baby.
I am usually anti-med for my dd and ds, but I agree with other posts that say when a baby is in serious pain, that is not a good thing. We tried Hyland's Tablets, Hyland's Gel, Nature's Remedy, Children's, and several other "natural" or homeopathic teething remedies and they didn't touch my dd's most severe teething pain; I found they were better for the more nagging pains of teething, not the acute, up-in-the-middle-of-the-night screaming. So I gave a half-dose of Tylenol (at 22 lbs, that's a little less than 1 dropper/0.8ml) when needed, which amounted to maybe a dozen doses during the couple of weeks she was in the most pain. I also did a lot of other remedies like having her chew on cold washcloths and so on. The Tylenol was a magic bullet though.
I agree that you should feel comfortable giving your baby a little Tylenol if you want. I'm not trying to say at all that parents who choose homeopathy are misinformed or whatever, rather that parents who choose to use Tylenol or Ibuprofen occasionally should not feel bad about doing so.
[Edited to add more background on my dd's teething.]