Is there a limit to how many times I can enter Thailand on a visa exemption or tourist visa in a year?

The limit of 30 day visa exempt entries by LAND is two in a calendar year

There is no official number of 30 day visa exempt entries you can get when flying in

BUT

after a few be prepared to get pulled aside to be asked what you're doing comin' here so much, why you're using visa exempt entries instead of another type of visa AND it can't hurt to have proof of onward travel showing you're leaving in 30 days