First I want to say that probably most of the things I include here will be dramedies, rather than dramas. In fact, it can be a tough call whether to call some of them dramedies or comedies, and there's a good chance some people would choose the latter. But I make my best guess for what genre is most accurate. Of course, there will also be some things that definitely are dramas, though most of the web dramas I watch will fit better in some other category, like science fiction than they would here. So... yeah, mostly this is going to be dramedies.
See also drama & dramedy shows, drama films, drama web films, and serio-comedy movies