Why is everyone going on about time travel? This is a video game! Video games COME with a save feature. So I can already go back to redo crap without the need to travel in time.
Sims 3
So easy to manipulate. I'd become an alchemist, make and drink 9001 skill boosters, make a witch's brew potion and drink that. I'd not need to rest in those 24 hours because I could just get an invigorating potion. Eventually I'd be able to perform magic that freed me from having to eat or poop or bathe. I'd also be able to turn a useless cookie into something that'll be worth 2k if cut correctly. Not to mention that the console commands completely break everything. I'd also learn how to make the young-again potion and build up a stockpile of the supernatural potions to sell them to people. 24 glorious hours is around 60 in-game days to make myself awesome...
Granted the witch thing would't stick around, but I'd still already have mastered all the skills of life. Then armed with the ability to do everything ever...
Grand Theft Auto 3
Listen, we're not talking about actually going into the video game, I wouldn't have to put up with the graphics. GTA3 is still my pick for the funnest of all the GTA clones... and the tanks were just awesome. They also had the cars that never stopped working no matter how badly you smashed them up and running from the cops was fracking hilarious.
Infamous
I, as the purple mage, cast lightning. I wouldn't be dressed like a normal douche like Cole Mc'Idiot. I'd ham it up. I'd be busting out the robe and wizard hat. And I'd definitely need the new power because the authorities would be nice and pissed at me for the tank rampages that happened the day before.
Civilization 4
Now that the world is sending entire armies after me because I'd have gone evil to get the chain-lightning thing, I'll need to ramp up my game a bit. So, starting as a single unit, I take over a major industrial city by walking onto it and killing the "police-officer" unit. I'd be able to do this because I can give myself all the promotions. Thus it becomes my new nation. Seeing how advanced, industrial, and over-populated we are, I'd switch to slavery and mass-produce a bunch of defendy tanks. I'd then abandon the city, letting America retake it and deal with all the unhappy survivors, and move on to a different city, probably in Canada. I'd hold on to this one, being better defended and all. In 24 hours (which could cover several centuries in which I somehow don't age or die) I could get people to follow me for reasons beyond "that's how it works in the game".
So now that I've got my own nation...
Xcom: Enemy Unknown
That's the best goddam research facility in the existence of anything ever. Too bad it doesn't bring the game's setting with it, but I bet I could make some massively great scientific breakthroughs even without alien alloys. I'll just "scan for activity" when trying to cram decades of research into 24-hours.
Pokemon... um... Emerald
This crap isn't going to stick after the "day" is over... so I'm going to get myself a bunch of those candy things to evolve my pet cat into "much cooler looking" pet cat and then stay in and watch TV. It might also be funny when people realize they've taken in dangerous animals as pets when suddenly the lovable "partner" thing dissolves away.