Answer:
That depends on the version you have. Up to Excel 2003, the standard amount of columns has been 256. They are labelled by letters. After Z you get AA, AB, AC etc. until you get to AZ. Then it is BA, BB, BC and so on. The 256th column is IV. There have been 65,536 rows, all numbered. That makes 16,777,216 cells. That was the case up to Excel 2003.
In Excel 2007 the maximum number of rows per worksheet increased to 1,048,576 and the number of columns increased to 16,384 which is column XFD. That makes 17,179,869,184 cells. Excel 2010 has the same amount or rows and columns.
Columns run up and down (vertical).
Rows run side to side (horizontal).
Version 12.0 can handle 1M (2^20=1,048,576) rows, and 16,384 (2^14 as label) columns.
Additional info: In Excel version 4.0 and earlier, the row maximum was 16384 rows. Also, there was only 1 'sheet' and they were called 'worksheets' (now they're called 'workbooks')