Ah, bosses. I like boss battles with a good storyline. Also I don't like bosses that are ridiculously out of proportion. My ideal boss is the player's mirror image in terms of level, power, ammo, etc, although perhaps a different class of character. Say the player is a level 20 swordsmaster, and the boss is a level 20 necromancer.

It is ok if they have about 1.5 hps the player has, sometimes even 2x is ok, but it is their AI that should make the difference, not the HPs. I hate it when you keep hitting the damn thing but your hits do 20 damage, out of 70,000. That's just trying to make a hole with a dessert spoon and it's ridiculous.

One of my favourite bosses was Max Payne's Gognitti, or Jack Lupino.