Just like purchasing a place the brokers/agents have to be paid for their service.
If they represent you and if they are finding you place that is being rented by individual owners they may also be getting money from the owner of the property, or splitting the fee with the owner's broker. If they are finding you a place that is owned by an apartment complex they might not get any fee from the owner because the owner is playing a management company for that service.
If the broker is working for the owner, they should be getting their fee from the owner. Yes you are paying for a portion of that fee in each months rent, but you shouldn't be paying that fee on top of the rent.
That type of fee certainly isn't unheard of... Brokers sometimes have access (or even contractual rights) to particular properties that you won't be able to get into otherwise. In my experience it boils down to the fact that it's the price you're going to pay for dealing with the broker.
Whether or not it is "unreasonable" is up to you and your willingness to pay it. I ended up paying something similar once in San Diego, and have paid more than that in Berlin to secure an apartment that was just right.
If the broker is worth the help they've given you, it may just be the price of admission to the property. It does kind of sound like you got 'sold' in the classic sense... you fell in love with the place and then they sprung a fee on you.
I would go back to the broker and express the fact that this feels kind of sneaky (it was...) and tell him/her that you're disappointed. If you haven't signed any kind of exclusivity agreement, I would also look somewhere else/with someone else in the area to see whether this fee is 'reasonable'.
Definitely not unheard of; in fact I've heard figures as high as 6 months' rent, basically splitting the first year's revenues with the landlord.
These apartment location agencies don't work for free. Typically, they make a deal with the landlord before you ever enter the picture, in return for the agency recommending the apartment to you. The agent's name goes on the lease paperwork, and they get paid. Often, the agent will take pains to personally be present for the lease signing so he can ensure the referral information is correct; otherwise he just gave his services away for free.
If the agent has not made an agreement with the landlord, they'll typically come to you for payment. Again, the agreement for such a payment is stipulated up front before they start showing you properties and consummated when you sign the lease (possibly with a "kill fee" of time and materials even if you don't sign with any property they show you), but now it's you on the hook. Typically, this arrangement is reserved for high-value properties like downtown condos, where the landlord doesn't need a recruiter bringing clients to his door; the name of the property itself is its own marketing, and they have a waiting list. However, you, as a wealthy but busy potential tenant, need assistance traversing the complex negotiation and contracting process, which the agent is only too happy to help you with, for a price.