+1 on checking the chain, also. Highest probability is that you've got a stiff link in the chain and as it goes around, it clicks.
Second thing is to check the RD settings. A click could mean that the derailleur is misaligned. Turn the adjuster barrel, either on the shifter, if you have one, or on the rear of the derailleur itself. If you dropped the bike on the drive-side recently, it could also be an indication of bent hanger. Lastly, if the bike is feeling mushy - it flexes a lot, check the chainstays just behind the BB. Step sideways on the crank to see if the right chainstay flexes and shows a crack along the inside. Stop riding the bike if you see a crack. It means the bike is indeed flexing a lot and shortening and lengthening the derailleur cable as you push hard.