Don't do it if you can help it.
If you have to, make sure the agent is someone who is in a serious position to make that exclusivity worth your lost opportunity cost. That means they have sales with books like yours. Recent ones. Do your homework here. A month is the longest I'd ever ever ever agree to exclusivity. Ten days (or two business weeks) would be ok.
And exclusivity is not bondage. If you send something on an exclusive basis, and the agent doesn't get back to you, fire off a letter withdrawing the exclusivity. You don't have to be nasty. Polite is a much much better choice. "I sent you my manuscript Miss Snark Debits Dallas on an exclusive basis on July 17. I hope it's something you'd like to represent. I need to move forward in my quest for representation and plan to send out query letters to other agents on September 1. I appreciate your time and consideration." Give them enough time between when you send the letter and plan to query others --two weeks or so. Make SURE you include an SASE with this letter!!!
I don't ask for exclusivity on anything. I'll ask you if anyone else is reading this. If they are, just tell me. It usually moves you up the list a little but, not much. If Binky Urban or Jenny Bent make you an offer before I get off my snarkie ass...it's my loss.