Unless you're upper management or have some high-level specialized skill set, the HH you'll get probably has no special connections and will work from the exact same job listings
If they ask for a fee up front, you're probably just paying them to email your resume to monster.com. State Attorney General offices across the country are always going after these people for claiming to have "secret inside connections" that don't exist.
(Note hiring your own HH is the opposite of the situation HotChic describes, where the company has hired someone to look for people like you.)