My parents are in US for the last one year. They got their GC in July 2010. They stayed with my brother most of the time and they stayed with me too for some time. They have SSNs.
My parents don't have any income.
Can me and my brother claim them as dependent parents while filing taxes?
Will both of us get an exemption of $3700 for each parent.
We both supported our parents financially.

If you provided more than half of the support of a parent, you can claim the parent.

I know I can claim my parents as dependents. Can my also claim them as dependents since he too spent a lot of money on them.

Each parent may be claimed as a dependent by only one person, and that person must be the one who provided more than half the parent's support. So if you claim both your parents as your dependents, your brother may not claim either one.