In my own limited travels in Europe I didn't run into any big issues, but then I didn't go to Oktoberfest, which is known to be all about meat. (Apart from the beer, that is!)
I have travelled a lot more in Latin America. At first it was more of a challenge, though in Mexico and Central America one can usually find beans and tortillas. These days most larger towns have vegetarian restaurants and of course touristy places always have some vegi options, though they tend to all copy each other.