This question depends on how you view 'tense' and what factors you consider to be a part of tense. Some people will tell you there are 3 tenses, some will tell you 2, others will tell you 12 or more! In my opinion there are only 2 true tenses 'past' and 'present'. The "future tense' isn't a different verb form, it's adding a model verb in front of a present tense verb.

Sixteen. But that doesn't include time travel or recursion.

Oh, there must be over a dozen. It's about the same as the number of indicative tenses in Romance languages. Let me see how many examples I can come up with, off the top of my head. I'm not going to try to look up what the grammatical names of these tenses are. I'm calling these "tenses" because they were called "tenses" when I was studying English in high school. They all have names, like "present perfect continuous." In English we often form tenses by combining extra words with the verb, rather than by changing the ending of the verb. I walk. I am walking. Tomorrow I will walk. By tomorrow evening, I will have walked five miles. I was walking yesterday. I have been walking all day. I walked to the store and back. I have walked to the store many times before. Yesterday, I had been walking for thirty minutes when my cell phone rang. Today, I have had so much walking that my feet are starting to ache. Yesterday, I felt good after I had had my walk.

There are 3 tenses. Past, present and future.