Well, I know that this is going to be controversial... But when I got my first rat, she lived alone for 8 months before I found a friend for her. I had her out of the cage for 3/4 of the day, and at night she ran on her wheel like a maniac. She always seemed perfectly happy, between the wheel, elaborate nest building, and her cage toys. At 4 months, I started taking her for regular playdates with a friend's girls, and they would happily tussle, chase, and hump each other. Now she finally has a permanent companion, with whom she sleeps & hangs out with only a tiny portion of the time. Honestly, I see no difference in my rat's personality. She seemed very content when she was alone, and just as content now that she's not.
However, I do realize that this is the exception to the norm. My girl had the luxury of being played with by a human constantly, since I'm a college student, have a loose schedule, and can easily study while using one hand to absentmindedly play with her. If she hadn't had so much attention, she probably would not have been such a happy, well-adjusted rat.
Granted, I'm not advocating having single rats. But in situations where they get excessively large amounts of attention, and have enriched cage environments, a single rat can be happy.
Of course, then you do miss out on the cuteness factor of rattie piles, gigantic multi-rat tussles, simultaneous wheel running, and silly hoarding behavior. Rats are definitely more interesting & cute in groups... especially 5+. Once you've experienced rat's awesomeness in groups, your biggest problem will be limiting the number you have.