How many records in one table can withstand myslq?

I believe that the author of the question is not worth asking the question, "How many records in one table can withstand myslq?", because it was originally wrong.
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Case (when the question is of purely academic interest) will not be considered.
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You should ask other questions:
— I just need MySQL to solve my problem?
— what I will be rested with a large number of records in the constraint record or on reading?
— what amount of memory the MySQL server will not be able to effectively dostupatsya the data?
— what is sharding, States for dividing and replication?
— how do I backup a database?
— what happens if my base will fall?
etc. in the same direction.

1.844 E+19 in a table of type myisam.
Have innodb harder to find, but there is a limit to 64Тб on the file, and therefore on the table.
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Only this knowledge you no practical benefit will not bring.

A hundred million keeps quiet, but of course the table is severely optimized for the particular quite simple query. InnoDB.
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To switch to another DBMS, probably not worth it. It is worth to measure how dire the situation is now and whether to change it. Analyze what queries are coming to the table, how fast they work, what are the main operations are (insert-read), there is this funny effects (for example, locks on MyISAM and InnoDB are very different) if all the indexes are, are there any extra indexes, is it possible to reduce them, etc. then be able to make a decision. Now if You have 1 million, you can score a test database of 5 million and see if much has changed alignment.

Saw 2 billion But it was mistakenly created, working with her was of course impossible :)

a million records is not much.
I have a couple of tables 1-1.5 million records, innodb, do not experience problems

do you need it? what is the purpose?

I have a table with 50 million rows, however, Oh I suffer with her.
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In General, many large projects running on MySQL, I think they have to order more so that there is no foreseeable limit, it all depends on configuration and hardware.