In 1995 Roger Schlafly found a very large prime number and then somehow managed to patent it! Can you really "patent" a number? Well, it seems the answer is yes, but legal issues aside the whole notion of pateting numbers lacks any sense, at least for me. So, are technological patents a good idea?
The central problem is that while patents might somehow encourage sharing information because at least everyone can see the patent and eventually the patent will expire (compare it with secrecy like the coke recipy that might never be known) the current "lawsuit culture" has gone to really funny extremes and some very nasty ones like software patents (you need to pay royalties for patented things like scroll bars, at least in principle).
I have just read an unbelievably funny story in this regard (even funnier than Sagan vs Apple), it seems that Kimberly-Clark was using some patterns quite similar to Penrose Tilings in toilet paper, of course Mr. Penrose (who has done many remarkable things in mathematics and physics) didn't liked such a close link with the lavatory and sued Kimberly-Clark! You can read an account here.
Personally I find that science belongs to everyone and there is no sense in trying to prevent it's widespread use, even in the lavatory.