Here’s a simple solution, using built in functions.
Start by copying the list, and pasting it in another column. With the pasted data selected, click on menu option DATA > Remove Duplicates. This will allow you to have one column with all values, and one column with unique values only.
In the Remove Duplicates menu, make sure you have selected the right column, and uncheck in case there is no header
A confirmation message should be displayed, showing how many entries and unique values the list contains
Then, next to the first entry of the unique values, enter the following function, to count how many times it occurs in the full list
=countif([column with full list];[first value])
See the first result, extend the formula to all unique values
And voilà ! Here the result is displayed, with number of entries for each value