Why get a chef's knife or santoku if I don't eat meat? If I don't eat meat, is there any reason why I would choose a chef's knife or santoku over a vegetable knife (e.g. Japanese vegetable knives or Chinese cleavers)?

I eat all kinds of foods (from mexican to chinese)  and make nearly everything from scratch (minus things like noodles), so from my cheap interim chef's knife, all I do is chop, slice, and dice. Although I've only recently taken up cooking, I don't see myself doing anything else (paring and bread knife aside). Because of this, I've been debating getting a vegetable knife, such as a Global vegetable knife or Wusthof Chinese cleaver.
Even for meat eaters, almost all knife work is done on vegetables.  Santukos and chef's knives are general purpose knives, with great utility on vegetables.  Chinese cleavers are also general purpose knives, the functional equivalent in that culture to the chef's knife.

The advice offered to you in this question:

Which knife is best for somone just learning to cook?

does not change simply because you are a vegetarian.