How many times can I enter Thailand by plane on a tourist visa without border runs?

What Brandon said.

"How long can I stay here on Tourist visas & border bounces" is like asking "how long is a piece of string".

The more such visas and stamps you have, the more likely it gets that you'll be questiined or potentially denied entry; all you can really do to mitigate this is have the Three Proofs ready (in paper or electronic) form to show them when you get to the airport/border crossing:

1) Accommodation 2) Finances 3) Onward travel (air or bus ticket).

There's no limit written into law about how many times you can enter Thailand without a visa by plane. You can do it until you can't. Each entry is at the discretion of the immigration officer you are standing in front of and if they think you are trying to live in Thailand without a long term visa, they are likely to ask you a lot of questions and to potentially deny you entry.