Are there any types of basil that are perennials in Ontario?

Basil is not a perennial anywhere except low desert or tropical areas. Most basils start wilting when the temperatures get below 40 and they don't grow well until night time temps are in the 50's. However, you can grow basil in a sunny south window in the house and winter it over for next summer. That way you'll be starting out with a larger plant. You'll need to cut it back in the spring so it doesn't get too long and leggy and flower before you want it to.