Some people think they are an indispensable part of dating. Others think it's a complete waste of time. The truth is somewhere in between.
On the one hand, I can't stand when people just send me a shidduch resume without telling me anything about the girl, a resume which sometimes will only have a list of schools, family, and references, and ask me "So, nu, do you want to go out with her?" I'm sorry but what you just sent me looks like every resume that's been sent to me in the past 6 months. You can't honestly expect me to give you an honest answer of whether or not I think it's a good idea to go out based off of looking at a resume for five minutes. Maybe you can tell me what you saw to think this a good idea, and at least give me the illusion that you did not just think: pants+skirt=shidduch.
On the other hand, I don't like when people just extol a girl's virtues and personality traits, without sending me a resume. I would like to know which sem she went to, what's her family situation, and if she's got a blurb describing herself and what she's looking for, it is somewhat useful in weeding out those people who are completely off the map.
BTW I also like the term "profile" a bit better than resume. Sounds less businesslike.