Should I put a surge protector on the 110v to my Trane furnace
I would recommend a whole house surge suppressor. They can be attached to your existing panel. If you have extra space in the panel and depending on the type of panel, you can get them that plug right into 2 side by side poles. Otherwise they can be attached to a double pole breaker. They come in various types and protection ratings. Of course the greater the protection, the greater the price. 

With as much electronic devices and coprocessors that are now in a residence. It doesn't hurt to have a little protection that could save you thousands of dollars. Even if you house is insured, consider the deductible and the hassle of replacing everything after a major surge and damage.

Good luck.