Third date. We exchanged clean STD results (so we could have sex obviously) and said we were going to exclusively see each other because we were interested in seeing where it was going.
But we'd had a chat on the first date about our general intentions (he said 'not casual but not necessarily planning to get married' - which is funny as we are now getting married!) and whether or not we were currently talking to or planning on dating anyone else and we both weren't. If we'd been dating other people at that point I imagine it might have taken longer but as it was we were both only seeing each other so we were all in quite quickly.
I've had relationships where we were just casually dating for a few months until we decided to be exclusive, so it just depends on where you're at.