The number one, definate, and in my opinion most important reason I prefer rats is their personality.  Rats are really closer in personality to a dog than the other rodents; in fact they're very similar to a miniature dog in personality.  They're friendly; they love being with you, they're always begging to come out of the cage.  They consider you part of the family in the same way dogs consider you part of their "pack".  They show their affection in many ways; first off, they just very obviously prefer to be with you.  They love to be scratched behind the ears; hyper-active females may not always have time for this, but most rats are quite content to spend at least some of their time curled up on your lap behind petted.  They'll even "purr" when content; grinding their teeth softly.  And they lick you, again very much like dogs!  Some rats will lick and groom you nearly constantly.  They also love to play; like the smaller rodents, they love to explore and are very curious, but rats also involve you in their play.  Young rats especially will play-fight with each and with your hand, much as a kitten will.  Here again, the usually more hyper females will often continue this into adulthood.
 

    Rats are by far the most intelligent of the small mammals.  They can fairly easily be taught a number of simple tricks; the most popular, and among the easiest for the rat to learn, is to come when called.  Others can be taught, as well.  Their intelligence no doubt contributes a great deal towards their personality, but it in itself also often attracts people!

Individuality:

    Each rat is a very definate individual.  They can be as different in personality as they can in color and size.  Besides personality (and obviously closely tied into that), it's one of my favoritet traits because I never get bored with them!  I've had litters of all the same color, visually indistinguishable, that I could tell apart easily (well, almost easily) just by the differences in personality.  Of course, sometimes it can be a drawback, if you happen to get an individual rat who's personality isn't what you'd prefer; but most of the time it's just darn interesting!

    Children's Pets:

    My own first memorable (for me) encounted with rats must have been when I was about 5 or 6.  We'd gone to the local pet store to replaced the most recently deceased hamster or gerbil and one of the pet shop employees took us to the back room to show us a litter of black and white rats, trying to convince my mother to take one of those, instead; it's my guess now that she'd probably gotten attached to them and didn't want to see them sold as feeders!  My mom, who at the time was still a bit afraid of rats, turned her down; but the baby rats and the employee's arguments for them stuck in my mind.
    Really, the rat probably would've been a better choice than the hamster, as a pet for us.  It is my opinion that rats make among the better kids' pets; first off, just their size can be a big plus; kids, small kids especially, are just much less likely to unintentionally hurt rats... Plus, they're considerably easier for them to hold, not being as small and slippery as the smaller rodents.  Their calm personalies also help in this; a rat just is going to stay more still, and be less likely to wander.  One of the big pluses is that rats do not bite; the average rat will, in it's lifetime, not bite a single time.  I would have a hard time to find a hamster or gerbil that would do the same!
    Another thing that makes it much easier on everybody; anyone who's kept rodents, and most especially rodents with kids, know they get loose sometimes.  They get dropped, or set down somewhere and forgotten about, or the cage door gets left open... Whatever, it happens.  With one of the smaller rodents, this generally means a long, drawn-out period of searching, mad dashes, and pulling out furniture.  I myself became quite skilled at catching gerbils while still very young.  Rats are a bit different; rats, when set down somewhere, are likely to sit there for a few minutes.  Even if they wander off, they just wander right back when they get tired of exploring.  When an excaped rat is sighted and approached, they do not make a mad dash to the nearest dark space; they generally just sit there calmly, wondering what you're up to; that is, if they don't run towards you!