Sean has some great advice below. To answer your question directly, there are not many (if any, I'm not aware of any) companies/brokers that represent renters. Property Management companies represent property owners.
Craigslist is by far the best resource I know available to you to find a property. But heads up: Vacancy Rates are EXTREMELY low right now. A Q1 2011 Report released this week has the vacancy rate for 1-4 Units (single family homes, duplexes, etc) at 1.5% in Denver. That is crazy low. Tons of demand for not a lot of supply.
Real Estate brokers are educated and licensed on leasing law. Most/none work in representing residential tenants becuase there is no/little money to be made. I might suggest that you find a friend who is a licensed Real Estate broker to help you review your lease and possibly help you negotiate. I know that I have done that for many friends in the past. If you do not know any licensed Real Estate brokers, shoot me an email and I'll assist you.
Once you know what area, then the second question is what building(s) in that area fit your needs, provide the amenities you want, and fit the budget.
I'd spend some time driving around different parts of the city if you have not answered question 1. When you have, then use Craigs List and general google searches to resolve the second question.
Some people like to go to "for rent by owner" because they think they can save some money, sometimes it works, but a lot of times going without a realtor becomes into a big headache, specially talking about the rents. Due to the huge amounts of foreclosures, it is always good to work with a Realtor so he can find out for you the status of the house you want to rent, and make sure it is not going to foreclosure. You can do that yourself also, you can find that information in the public records of your county or county clerk. I would suggest you to find a Realtor with experience in your area. Have a great day!
I would try Craigslist, very carefully, I might add - DO NOT send money anywhere. Meet the owner there, check public records to make sure that the person you're dealing with is actually the owner, and then ask for a copy of the lease so you can review it. I would ask experienced friends for help reviewing the lease, maybe a real estate agent will help you (I'd be happy to review a lease for you for no charge).
Best of luck!