I play Metroid, Final Fantasy, Halo, Elder Scrolls...pretty sure there's a lot I'm forgetting about here.
As far as speedrunning goes, the only games that I really speedrun are Super Metroid and Final Fantasy IX because I get something (relatively) tangible out of it. I usually take my time to enjoy a game when I first get it, play it normally without a guide, then after that I go straight to GameFAQs and find all the secrets I missed. I play through the game a few more times until I get bored of playing it *normally* (which nowadays is very quickly). That's when I start with the challenges.
I'm not actually a speedrunner, I'm just a challenge gamer. These go hand in hand, though, and before I know it, I end up on ZSR. Perhaps someday I will do some real speedrunning, but for now, this will have to do.
I prefer low% to any% simply because if I can complete a game without any unnecessary items, I have the skills to take on anything it throws at me. My original concept of OoT low% was when I saw Manocheese's Uber Challenge guide on GameFAQs. I learned the tricks and completed it. I figured that it was low% without item use restrictions and without the Giant's Knife (Broken). His constant reminders in the rules that the player must get ALL Medallions seemed to imply that you weren't technically required to have them to beat the game, but I eventually forgot about it until a GameFAQs member confirmed that only Shadow and Spirit Medallions were needed. Then I started a topic there to theorize on what low% would actually be, and then ZFG pointed me to ZSR, where they have ISG, bomb hovering, RBA, and TP SBs (including the awesome EMS).
I also liked low% because to me, it was a faster form of perfection. 100% runs took too long (at least for me) and the end result of any%, was...well, any%. Something somewhat random. I didn't like that. Now that I've seen a few 100% routes, I do them somewhat casually (just so I can fully complete a game in a reasonable amount of time).
Final Fantasy is a bit different. Instead of low%, I do low level challenges (or low EXP really). I usually add restrictions like low AP, no extra skills learned (e.g. Limit Breaks and whatnot), basically anything that you could grind. I did a lot of grinding when I was a kid, and this is probably to make up for it. But because I want to have 100% files for those, too, and because playing through the game takes so frickin' long, I tend to always get the missables no matter how much forced EXP I have to take with it. This is where my OoT low% w/ Forest Stage nut upgrade and w/o RBA came from. And only without RBA because at the time we didn't know that you could get sticks back by buying them. I abandoned this idea for adventure games after seeing how fast 100% runs can be done, but I still keep them for Final Fantasy playthroughs.
Halo doesn't really lend itself to speedruns or challenges (at least not the way we know them). It doesn't really have sequence breaks. I challenge myself with Legendary playthroughs, but that's about it. If I can get my Call of Duty skills up to scratch, I may start making videos of 3-star Special Ops missions from Modern Warfare 2.
Elder Scrolls doesn't really fit our challenge/speedrun profile either, but I enjoy playing as Elminster. Basically I play an unarmored mage with a sword. I like the depth of sidequests in that game, and the customization of weapons (although there's no option for a longsword that deals Sonic Damage. FML).
I usually focus on one or two games at a time, perhaps growing bored of one eventually and switching to another. I haven't even finished all the new games that I have, because I'm so attached to the old ones - and because I still haven't finished doing challenges for them. I'm currently working on
Metroid Prime 22% hard mode.