In 4X games, such as Space Empires and Master of Orion, my favorite part of the game is researching new technologies for my empire. I especially like when the tech tree is randomized from game to game, as in Sword of the Stars and Master of Orion (if you're playing an Uncreative race).
On a (seemingly) unrelated note, I don't like to play roguelikes that are not under active development. Somehow they seem "stale", even if the game mechanics and UI are perfectly polished. I'd play Dungeon Crawl Stone Soup over Nethack any day! (Well, that's not the only reason, but you get the point. I'd use ADOM in place of Nethack since it's more polished, but, well, ADOM is kind of under active development again...)
It never occurred to me until now, though, that these two concepts could be related. I guess you could divide people into 4 categories (named after the 4 X's) based on how they get enjoyment out of games.
Explorers (that's me) enjoy playing games to discover new things - new game mechanics, new unlockable features/characters/weapons/whatever. They tend to be completionists, although explorers may also complete a game 99%, then decide that that last 1% is too hard to bother with.
Expanders are also completionists, but unlike explorers, 100% completion is their primary objective. An expander will not stop until every last bit of unlockable content is unlocked. They don't really enjoy actually playing the game as much as explorers do - instead they get a huge adrenaline rush at the end when they finally complete everything.
Exploiters are minmaxers. Not content to have a +10 sword of awesomeness, they will find loopholes in the rules to get a +11 uber miracle sword of awesomeness and slay everything. They draw enjoyment from the process of devising these schemes, and also somewhat from laying the smackdown on opponents with their cool toys.
Exterminators, of course, are in it to win it. An exterminator is not happy unless he eradicates every last one of his opponents. Exterminators might also like to taunt their opponents and kick them when they're down. They absolutely hate losing, obviously.
Actually, I guess you could pretty much equate these categories to the "classic" 4 categories of gamers:
Explorers = Real Roleplayers
Expanders = Loonies (the weakest correlation of the bunch - hey, someone had to be Loonies!)
Exploiters = Munchkins (obviously)
Exterminators = Real Men
Maybe I should get into some D&D sometime, if I'm that kind of player...