What parasites, if any, am I susceptible to if I eat sushi?

There are several. Hopefully any restaurant would adequately prepare your food before serving it to you but you are right to think that raw meat, in this case fish is riskier than cooked food. There are several parasites possible in raw fish. One example is diphyllobothrium, a tapeworm that while treatable can cause nausea, weakness, diarrhea and others.
Fish tape worm. The main one is sushi worm or diphyllobothrium latum, the fish tapeworm. It is acquired by eating raw or undercooked freshwater fish such as salmon.