Whilst I am currently not fortunate to be in a paid position for doing my creative work, I am seriously considering starting commissioned, freelance work in order to produce work out of my comfort zone, rather then do requests for friends/relatives/whoever wants it.
I have just recently finished a project for a client- and do not ask me who this was, as the work has not been made public yet- through Mandy.com, and I have been able to get confidence in what I can provide to people as an artist. This confidence has made me feel I can apply for work that I would not have even considered, and has encouraged me to work on my portfolio, and website, to promote what I can do to get paid work. This work might have been, at the time of writing this, done for 'free', but I feel potential clients/employers/agencies will want to see what you have done, rather then what you can do. They want to see the 'experience', and if they do not see this, then you are going to keep getting the same generic response of rejection from them.
Whilst I agree with Silver's remarks about doing free work, I feel that you need to get your foot in the door by doing work people will want to see from you, rather then what you want to do. It is something that cannot be taught to you from an establishment, and you need to get the experience of finding out what you are capable of doing by removing yourself from your comfort zone. I would not have produced some of my most prolific projects without doing what clients wanted from me.
Overall, during these financially awkward times, you need to prove others that you can produce work of a profitable quality, nothing says that better then providing proof that you have done this kind of work before. So go out there, find the work you can whether it is paid/unpaid/voluntary/contractual, and get that experience under your belt.