Some national cuisines (Indian, Thai, Vietnamese, etc.) have a strong tradition of vegetarian cooking, and thus offer a large choice of non-meat dishes. You can, however, enjoy vegetarian options in pretty much every type of cuisine, even ones that are traditionally meat-based. There are two ways to go about this - either find dishes that are traditionally meat-free (every cuisine has these), or, if your favorite dish requires meat, substitute the meat with something else. You'll find that a simple substitution goes a long way. And the internet is full of tasty vegetarian recipes.