Everybody gets one personal exemption, worth up to $4,050 for tax year 2016, either as a filer or as a dependent.
Because you're already getting your exemption as a filer, the IRS won't let you claim yourself again as a dependent. Same for your jointly-filing spouse – their exemption is already accounted for on your return, and putting them down as a dependent (even if you support them 100%) would be double-dipping.
And if you're filing separately, your spouse will claim their exemption on their return, unless they're:
Not filing a return;
Have no income; and
Aren't being claimed as a dependent by someone else.
In that case, you can claim your spouse's exemption on your return.