the most popular choices are: mysql ,postgresql, oracle and informix. (those are the ones I hear most about)
1) mysql: fast, easy, but limited SQL functions.
2) postgresql: slightly slower than mysql (7.0.3 anyway), more complex to set up,but much more powerfull SQL than mysql.
3) Oracle: fast, powerfull, extremely expensive
4) Informix: fast, powerfull, extremely expensive
1 and 2 are free, which means you don't get any official support you can
fall back on. If your DB kicks the bucket, you can't call a support guy to come over and fix it.
3 and 4 are close competitors in the "professional" market.
If you're not looking for some special features it's really down the pricing.
And pricing is... well... their price for an internet licence is more than the average price in the lottery.