I'm going to go with a guinea pig!
While very social like the famed rat mentioned already, guinea pigs really do associate with their owner and will greet with squeaks and playful jumping upon seeing their owner. Plus, giving them floor time to play around freely is fun for all, because they are a little bigger than rats and can roam around more with slightly less worry, and they are a joy to watch!
While not the most intelligent things in the world (rats beat out in this argument!), guinea pigs can be litter trained, and also some simple tricks if trained with treats.
They love to cuddle and are as curious as anything, plus they enjoy (and require!) a salad to complement their pellets and hay, so while making dinner you can toss in lettuce and assorted veggies and watch your bud enjoy it like you!
They aren't smelly, and while they poo a lot, it's little work at all if you've potty trained (and even if you haven't, guinea pigs tend to "do their thing" in corners, so a simple spot cleaning is all you need!) A good rule of thumb for the cage is that there should be 2 square feet of room per pig, but it isn't uncommon to get some Cubes and section of a part of a room, add a pan with some bedding (carefresh, or aspen... no pine or cedar), some toys, and let them roam and have a good time!
I can see that the rats are dominating the conversation, and while they are great pets, I just thought I'd introduce another lil' guy
PM me if you have any more questions about 'em! (I'll leave the rat questions to the experts