[count] count distinct values in spreadsheet

I have a Google spreadsheet with a column that looks like this:

City
----
London
Paris
London
Berlin
Rome
Paris

I want to count the appearances of each distinct city (so I need the city name and the number of appearances).

City   | Count
-------+------
London |  2
Paris  |  2
Berlin |  1
Rome   |  1

How do I do that?

Not exactly what the user asked, but an easy way to just count unique values:

Google introduced a new function to count unique values in just one step, and you can use this as an input for other formulas:

=COUNTUNIQUE(A1:B10)

This works if you just want the count of unique values in e.g. the following range

=counta(unique(B4:B21))

You can use the query function, so if your data were in col A where the first row was the column title...

=query(A2:A,"select A, count(A) where A != '' group by A order by count(A) desc label A 'City'", 0)

yields

City    count 
London  2
Paris   2
Berlin  1
Rome    1

Link to working Google Sheet.

https://docs.google.com/spreadsheets/d/1N5xw8-YP2GEPYOaRkX8iRA6DoeRXI86OkfuYxwXUCbc/edit#gid=0

This is similar to Solution 1 from @JSuar...

Assume your original city data is a named range called dataCity. In a new sheet, enter the following:

    A                 | B
  ----------------------------------------------------------
1 | =UNIQUE(dataCity) | Count
2 |                   | =DCOUNTA(dataCity,"City",{"City";$A2})
3 |                   | [copy down the formula above]
4 |                   | ...
5 |                   | ...

=UNIQUE({filter(Core!L8:L27,isblank(Core!L8:L27)=false),query(ArrayFormula(countif(Core!L8:L27,Core!L8:L27)),"select Col1 where Col1 <> 0")})

Core!L8:L27 = list

=iferror(counta(unique(A1:A100))) counts number of unique cells from A1 to A100