We always wanted three - no idea why, DH and I are both one of two. But there just seemed to be a glorious completeness about three that you don't get with just two DC. Even now, eight years on, I still love signing cards etc from us as a family and writing down three children's names
which sounds stupid but I do. I can't remember making an actual decision because we just always planned to have three.
I love the juggling act of managing a bigger family, but I'm naturally very organised so I definitely thrive on that kind of busy atmosphere. The only negative for us was the 8 year age gap between DC1 and DC3 as it's too big really (we hadn't bargained on fertility issues which left us with a big gap between DC1 and 2). So I'd say if you're going to do it, ideally don't have a gap bigger than 5/6 years between oldest and youngest, because DC's needs and interests are just so different, and for a period of time the older they get the harder it gets.
I found it hardest when the eldest was a young teen - too young to be left home alone but far too old for the kind of activities the younger ones enjoyed. Equally, the younger ones were too little to join in with the kind of activities the teenager liked. That is getting a lot easier now they are all older though and the relationships between them are developing and changing all the time.
I do agree with the point that others have made about finances. The world is still very much geared to families of four, and I think if you don't have a decent financial cushion it could be very tough. We are very lucky in that DH is a high earner so finance hasn't been an issue so far - the bigger car was affordable, we have a house big enough for everyone to have their own room, we have investment plans set up to cover uni fees, support with DC house deposits and so on and we can cover holidays and treats without scrimping. I do realise though that we are incredibly fortunate to be able to do this, and our situation is very much not most people's reality. I think if finances had been really really tight for us then we might have thought twice about having a third.