Is there a limit to the number of data records I can store in a table?

There is no limit to the number of records.
There IS a table size limit of 500 MB per table.  You can view your table sizes in 
Settings
App Management
App Statistics

However, depending on the number or relationships and summary fields and number of fields, as you get into record counts above 50,000 records you may start to run into performance issues.  ie 200,000 may be fine for a simple table with few relationships and 50,000 records can be a problem if you have 500 fields and lots of summary fields.

In other words, while the table limit is 500 MB, you may or may not run into performance issues before you hit that hard limit.