It depends on the person and on the baby, I guess. I've been feeling my LO move around since about 16 weeks, and just this week (I'm 21w+5) I've started noticing visibly when LO kicks or punches especially hard. My LO is CRAZY active though, and I'm betting s/he will be an amazing dancer or athlete, haha.
But yeah, I'd say it's probably different for everyone. If your baby's not all that active, especially, it might be a bit longer for you.