After working on the Giant Bomb wiki, I've learned that I have a fondness for games that give names to their enemies and bosses and show it in-game. The best example in recent years I can think of is Okami. Every imp, wheel, spirit, and emperor of eternal darkness was introduced with an awesome painting and had a name to go with it in the bestiary. A few re-releases of games have been adding a section in the game where you can scroll through the list of unfriendly faces that try and kill you, like Chrono Trigger. In some extreme cases, like Star Fox 64, the only way you can really find out what everything is named is with the help of a player's guide where there are pages and pages of info on the biggest weapon and the littlest fighter that ever crosses the screen.
 
I just find it better that a name goes with the character. I don't care if it's something dumb like "Crazy Flailing Ax Guy Who is Also on Fire, Dude". As long as it/he/she has a name. Mega Man is probably the master of this with sheer simplicity. Which one is Fire Man? Probably the guy who is shooting fire all over the place. The lesser enemies had names but you would never find them in game, but at least the bosses were covered. It doesn't guarantee a good game, but the polish is nice. It also helps share your frustration with other people by quickly identifying a lame boss or enemy. Helps with communication too.