The vegies that my mum generally put in were: peas, corn, carrots, beans and potatoes. Personally, I like to use all of them plus add pumpkin and sweet potato and you can even put in broccoli or pretty much anything. I think my brother made some while I was staying with him that had squash in it. oh, and or course you cook the meat in onion.

I don't think it's really achievable to make gulyas without meat, since it's by stewing the meat at the beginning of the process that you get the flavour of the dish. Anyway, it'd hardly be a Hungarian meal without some sort of meat in it - even bableves (bean soup) is made with a base of meat.