I've been thinking about this for my site and I've decided to set a minimum number of characters for a username so that it stands out as being a username rather than a random set of characters.

I think if you allow 3 character username people are more likely to use things like 'asd' and 'qaz'. Then on a site such as HN where you have comments labeled by username it can become confusing if all comments are labeled with garbage. Whereas if you set a minimum of 5 characters then people are more likely to user human readable words rather than garbage.