Elance is how I formed a relationship with one of my current clients. Ironically, I bought a considerable amount of bidding credits and used them all but got zero jobs from it. However, literally a few months later, I was invited to bid on a project by a client wanting some gift vouchers designing. I decided to buy some credits and bid and won the job, even though I wasn't the cheapest.
Since then, my client and I have a good working relationship and I've done other things for them.
That's the positive side of things.
The negative aspect of Elance is that, as Peter says, there are designers on there willing to do grand-scale jobs for $50. And of course that doesn't necessarily mean they'll do it well, but the client doesn't know that. You also have many Eastern freelancers/studios pitching for the same jobs, which can affect things too. And of course you have the client themselves who may only be wanting to spend £2.50 on something instead of £2,500!
The other downside is that you have to pay out money for the right to bid on projects you may not even win. In fact, there's a good chance you won't win the majority of your bids so it will feel like a waste of money.
Also, again as Dave says, there is Elance's commission fee but you can easily get round this by choosing to deal with payment offsite if the client is comfortable with it. There's only a few clients who wouldn't be happy with it.
So, in conclusion, Elance is a great place to find opportunities to work, but a difficult place to win it. You need to be patient and you also have to accept that you may lose money to begin with. It's your choice!