You're about the age that most folk have their first 'adult' relationship. Not saying first boyfriend/girlfriend, but rather the first such relationship that's conducted on a reasonably mature and happy level. I guess if you think of each relationship as involving some learning and some sitting back and enjoying, then around 20 is the first time that you get to spend more time enjoying relationships than you do learning in them. Most folk are a lot more hesitant in using the word 'love' as they get older - a 3 month relationship with hormones, tempers and moods going wild can seem like a really major relationship when you're a teenager, but later you start to realise that you don't really get to know a person you're with until AFTER the initial 2-3 month 'good behaviour' period is out of the way, and you both start being yourselves (rather than trying to impress each other).
It's also when most gay/bi folk I knew started coming out of the closet (even 10 years ago, the world was VERY different regarding homophobia).
Also, don't be overly worried if there just aren't folk around who you're interested in. Some people aren't straight OR gay OR bi - they've just got ultra-low sex drive (sometimes physically, sometimes in terms of not finding anyone they care about, sometimes both) and very few people interest them in that way. I've known a couple of people like that of both genders, and they certainly don't seem to have led unhappy lives because of it - if anything they tend to be a little more stress-free than most.
As for answering the topic question, then yes, about 5 times, 4 of them being women, 1 being a guy, and including my wife. Been married for around 3 and a half years, been together for around 5 and a half years in total. Next longest relationship was 3.5 years, when I was at uni through to the year just after I graduated, next longest after that was only 1.5 years. Only been 'in love with' someone I wasn't in a committed relationship with once - we had an on-again off-again fling over about 6 months, and had been friends for a couple of years before then, but were never 'a couple' per se.
Re: the 'she's moving to your house today' - personally, I was never much for the 'moving in' thing. I never lived with a g/f or b/f (lived with friends, just not 'that' kind of g/f, b/f) until I got engaged. Not saying that as a criticism, just personally I'm really really big on having my own space and my own freedoms. I'd make it fairly clear early on that I'm someone who's happy to spend lots of time with a partner, just as long as I get to go back to my own place, where I can watch TV or play computer as I want, not worrying about how I look, etc (i.e. quality time with them, but not the random watching tv on a sunday afternoon stuff).