>If you want to use your PC with two monitors, how important is to have both of the same size? The reason I am asking is I have now one monitor (23") and want to add another one. But I don't have much room on my desk for another 23" so I am thinking of getting a 19" monitor as the second one. Will it be a problem?

It should not be a problem. You will likely have different resolution on each screen, but you can use the smaller one for extra stuff you aren't concentrating on.