I lived alone for some time and literally had one of each dish (plate,bowl,cup,knife,fork). This meant that I had at most one dirty dish of each kind, and in general washed them immediately after use. In that case, it would have been pointless to have a dishwasher and it just would have been a buffer to hold more dishes.

Circumstances are different now and we dirty a dishwasher full every day, so it's definitely worth it to have one.

Overall, it depends on how much you dislike washing dishes, and how many you own. If you're single (which the fact you've posted this question on HN suggests though I don't jump to conclusions), I recommend owning as few as possible and just cleaning them as soon as you finish eating.