Some grammars say there are 2 verb tenses, the present and the past.

Other grammars say there are 3 verb tenses, the present, the past and the future.

However, most say that there are 12 tenses (see below).

I have never heard that there are more than 12 tenses. 

                  Example of the 12 Verb Tenses

VERB TENSE SENTENCE EXAMPLE

Present Simple I write

Present Continuous I am writing

Present Perfect I have written

Present Perfect Continuous I have been writing

Past Simple I wrote

Past Continuous         I was writing

Past Perfect I had written

Past Perfect Continuous I had been writing

Future Simple I will write

Future Continuous I will be writing

Future Perfect I will have written

Future Perfect Continuous         I will have been writing

Richard has given an excellent answer for the traditional 12 tenses.

English grammar combines tense, aspect, voice, and mood.  However, only a linguist normally cares about these details.  

Occasionally, combinations are counted as tenses.  For example 12 basic tenses in active voice and 12 basic tenses in passive voice are sometimes counted as 24 tenses.

The following examples mix and match the basic tenses for a variety of meanings.

- Joe said that he would come for a visit (he would come [modal would + present simple] = future in the past)

- Joe would come for a visit, if he were available (would come [modal would + present simple] = conditional result; were available [subjunctive of to be] = condition)

- Joe will come for a visit, if he is available (will come [future simple] = conditional result, is available [present simple] = condition)

- Joe said that he was coming for a visit (he was coming [past continuous] = future in the past)

- Joe was coming for a visit when his car broke down (he was coming [past continuous] = incomplete action in the past, broke down [past simple] = completed action)

- Joe cooked this chicken on a barbeque.  (cooked [past simple] = completed action)

- This chicken was cooked on a barbeque.  (was cooked [past simple of to be + past participle of to cook] = completed action in passive voice)