I have 2 favourite stupid rope tricks. One is the Texas figure eight, you hold the end of the rope in one hand like a dart, the other hand holds farther along the rope so there is a largish bight hanging between. Give the bight a twist so it spins around twice and toss the end through the hole, voila, a figure-8 to tie in. The other trick is the one handed bowline on a coil.
Another rappel trick I have heard: suppose you reach the rope end (double rope rappel) a few meters shy of a safe touchdown. Spin yourself around a whole bunch of time so the two strands twist around each other, lock off one strand and let the other slip through your device. You'll start unwinding and the friction of the ropes together will (hopefully) slowly let you down.