One of my favourite webcomics, Saturday Morning Breakfast Cereal, recently updated with a brilliant strip relating to this particular annoyance.
To be honest, this one doesn’t particularly bother me. The key is in the difference between the nominative and objective cases for nouns in English – and in 99.9% of circumstances, words in either case have exactly the same form.
However, there is in fact a relatively easy way to know whether you should be using who or whom in any particular sentence:
If you can replace the person in question with “he/she”, use who. If you have to use “him/her”, use whom.
He went to Florida for the weekend: Who went to Florida for the weekend?
The bell tolls for him: For whom does the bell toll?
So there you go: who is to whom as he is to him. Replace the words in a sentence and see which one sounds right.