It's possible you're being too hard on yourself—after all, you're not a sole practitioner who can pick or choose what kind of clients you choose to represent. Since you're currently the “low man on the totem pole” at your firm, it's only natural that senior partners will throw you cases they don't want to handle themselves—and you'll probably continue to receive these cases until a new junior associate is hired on.
Still, there are some things you can do to increase your prospects of being assigned to a big (or, at least, medium-sized) case. Rather than complain about the small cases your partners give you, handle them quickly and expeditiously, and then make it clear that you're after bigger game. The senior associates at your law firm need to be convinced that you're a competent attorney, and they will hopefully be so impressed by your efficiency (and your positive results) that they throw more challenging cases your way.
There's also nothing wrong with showing a little bit of initiative, and going out on your own to recruit high-paying clients with interesting cases. If you proactively recruit new clients, your senior partners will be more likely to assign you to their cases—though not necessarily as lead counsel, which is only fair given your junior position.
Recruiting more lucrative clients serves two purposes, of course. It gets you noticed by the senior partners as an attorney hungry for bigger challenges. And following through on these cases to a successful conclusion becomes a way to help promote your law firm, while establishing yourself as a good team player.
The one thing you don't want to do in this situation is to uncomplainingly, and invisibly, take on every low-level case in your firm; if you get too good at this, your senior partners may typecast you in this role and you'll never be assigned an interesting case.