Of course, there's a catch. Do you think if the offered unlimited storage, they would have it for very long? However, it's not that bad a catch, I'm certainly satisfied with it:
How can Yahoo! afford to give away unlimited email storage?
By hiring outstanding engineers, of course! Ours have been hard at work developing an incredibly efficient backend storage system. Protected by responsive anti-abuse controls, this updated storage system gives you the option to never delete another email! Unless, of course, you want to.
Basically don't hold your files in there to store them. I can live with that.
The purpose of unlimited storage isn’t to provide an online storage warehouse. Usage that suggests this approach gets flagged by Yahoo! Mail’s anti-abuse controls.
Unlimited storage gives normal email account users like yourself an opportunity to not have to worry about hitting a storage limit. Basically, the idea is that now you can save your correspondence and memories and never worry about deleting older messages to make room for more.