The rule about it comes from a rather strained synthesis of Latin grammar, though Latin infinitives are single words. It has always been done, so I would say it's OK. In formal writing, it is probably better to play safe and avoid them where possible, but otherwise I see not problems with them. Also, a split infinitive can provide an additional meaning:
I decided to not do it.
I decided not to do it.
To me, the first sentence carries extra volition and rejection, rather than simply not doing it, so I think there's a perfectly good case for it. I have also noticed that many people nowadays split infinitives to keep an adverb near the verb rather than right at the end of the sentence, which is presumably done for reasons of clarity.
Here's a common sense article from a newspaper copy editor on the subject: