Can I make risotto without wine?

Yes, all it is, is flavour.

Apple juice and grape juice are 2 things I've used in the past for non-alcohol people. You can also get away with not using anything as a replacement as long as you use enough of everything else (butter and Parmesan etc).

Wine just gives a little depth and a sort of 'freshness'.

Edit:

I just read the vegetarian part of your question. I'm assuming you already know, but Parmesan isn't vegetarian, as it is made from rennet (rennet is extracted from the lining of the inside of the stomach of mammals), and most commonly from the fourth stomach of young calves. The vegetarian substitutes I've tried in the past (Called pasta cheese), are not great. However, unlike Parmesan, Gruyere is allowed to be made with vegetable rennet and tastes great (I personally prefer it over Parmesan).

I've made risotto plenty of times without wine (as it's not something that I typically keep in my house).

The main issue is that wine is both acidic (which can affect how quickly things break down when cooking, like onions), and it's a solvent (so it helps to distribute other flavors). Although it does add some flavor on its own, you typically won't miss it.

Personally, I just use extra onions, and sometimes add a splash of a sweet vinegar (rice or cider) with the first addition of liquid.

I don't use butter or cheese in my risotto, as I find that those can dull some of the other flavors.

You can usually substitute vegetable or meat stocks for the wine/alcohol in savory dishes.

It's not necessarily the wine that is necessary, it's more of the freshness and acidity. You can imitate this by adding a little bit of citrus (lemon) to brighten it up. Fresh herbs may help too!

Since I'm a picky Risotto eater, I usually only make the one kind of flavoured Risotto (Cranberry,Mushrooms, Ramson, PineNuts,S&P) & I use my granny's foundation recipe, that does calls for wine, but she and I both substitute the wine with juice made from Elderberries. But if I don't have EBjuice at hand, I add a splash of Lime or Lemon, and up the broth for liquid and acidity.:)

I have an Italian recipe that my mom had and her mom had and it goes on and on. I have never seen any recipes online that has my moms and I'm surprised. It is a great creamy risotto and I make it. I'm a full-blooded Italian. My dad was and so was my mom. This risotto is the best I have ever had. It doesn't have wine in it. I make a sauce with my spices. It's only 1 can. Most people just use wine. I think sauce is much better. I boil a chicken for the broth. I add the rice to the sauce in a large pan. I continue to add the broth to make it thicker. I stir steady on medium for 45 mins. straight and at the end I use Asiago cheese after I grate it. The meat in my sauce that I use is gizzards. It has the best flavor ever.