Standard amount of columns (going vertically across) has been 256. Labeled starting with A through Z. After Z then the columns continue with AA, AB, AC etc. until you get to AZ. Then the columns continue through IV, which is the 256th column.
Standard amount of rows (going horitzontally up and down) has been 65,536 rows. The rows are numbered by sequential whole numbers starting with 1, 2, 3, etc, etc.
The total number of cells is 16,777,216. (Excel 2003)
Excel 2007 and 2010: The maximum number of rows per worksheet is 1,048,576. The number of columns is 16,384, which totals to 17,179,869,184 cells.