Yes, and the rate depends on the amount of ordinary income you have (including short-term gains) and the amount of long-term capital gains. The capital gains rate is 0% under $40k (for single individuals) but ordinary income is calculated first (after deductions) and the total income determines the bracket. So if you have $40k or more in ordinary income (after deductions) then the 0% rate won't apply to any of your long-term gains. If you had $20k in ordinary income (a.d.) then the first $20k of long-term gains would be taxed at 0% and the next $400k (from $40k to $440k of total income) would be taxed at 15%, with anything beyond that taxed at 20%.

Also, if you have significant income from investments then a surcharge of 3.8% in Net Investment Income Tax may be added on top of the long-term capital gains rate for part of that income for a marginal rate of 18.8% or 23.8%.