I was recently playing Parodius (パロディウスだ! －神話からお笑いへ) and decided that one of the most difficult (non-optional) bosses that I have encountered in gaming is the blowfish at the end of the underwater stage. Each time you shoot it both it and the thorns that it shoots expand in size, leaving you guessing at what point will the dang thing be destroyed.
Other bosses that I have faced that are worthy of mention are ones that I can't recall now (ie, a bunch from Final Fantasy V, and one from Chrono Trigger), but in your experience, which have been the most challenging of the games you've played?
Optional bosses are for instance, the Emerald and Ruby Weapons in Final Fantasy VII, and the Omega Weapon in Final Fantasy VIII.