I'm just going to bypass the discussion about who should and shouldn't have children, and for what reasons, and go straight to answering the OP!
I use the Mirena IUD. I'm on my second one and it's lovely. Hormonal birth control did NOT work for me; it increased my migraine activity and made me extremely emotional. The Mirena IUD is considered a "hormonal" IUD, but the hormones don't enter your bloodstream, rather the hormones only affects what it's actually physically in contact with.
The Mirena has been a great choice for me. My period was always very heavy and obnoxious and now I don't have them at all (not everyone with the Mirena stops their periods entirely, but it's not uncommon either). And you just never, ever have to worry about pregnancy. I think it's more effective than sterilization. Nothing to take every month...nothing to forget to take every month. Nothing to have to make a doctor's appointment to renew every 90 days, etc.
It's also extremely cost effective. I had to pay for my IUD this time around (not on awesome school medical insurance anymore and Canadian health care isn't advanced enough to cover such things. As it was, I paid 300$ for it and it's good for 5 years. I had my last one in for 4 years and only had it replaced prematurely because I knew it would be coming to the end of its effectiveness while I was overseas and didn't want to deal with the hassle of trying to find a doctor, or worrying if they even had the Mirena over here. This way I'm good for another 5 years. And, if you break it down by month...it's probably the cheapest birth control available. The only financial obstacle being that you have to have the 300$ up front.
The only other obstacle I know of is that doctors can have a pretty strict idea of who it is suitable for. Everything I've read from Mirena says that it is recommended for women who have already had one child and are in a stable, long-term relationship. I don't know if they claim you should have a child first because a) it makes insertion easier or b) they're afraid you'll use it and then never have children, thus slowing population growth (ok, I'm not going to go into my conspiracy theories...). But, either way, I don't think it matters. The doctor I saw was more than happy to provide the IUD to any woman who wanted long-term birth control and was compentant enough to know that it didn't prevent STDs.
And, for the record, I haven't had children and the insertion was no problem, so that kinda blows that theory out of the water. You take some ibuprofen and tough it out for 3 minutes and you're good for 5 years.