TeamWin Recovery Project (TWRP) - This is a very widely used custom recovery. It is fully touch-driven, has one of the most complete feature sets available, and uses a themable UI. TWRP is maintained by Ethan Yonker (Dees Troy) and sees a number of contributions from the community via OmniROM's code review.
ClockworkMod Recovery (CWM or CWMR) - This is one of the original custom recoveries that is still widely used today. Most of its functionality was written by Koushik Dutta (Koush), but it has since seen significant code contributions come from the community via CyanogenMod's code review. Several variants are available, including: standard (hardware keys navigate the menus), swipe (basic up/down/left/right navigation by swiping), and touch (fully touch-driven menus). More information on ClockworkMod usage can be found at ClockWorkMod Recovery Instructions.
Active Development: TeamWin Recovery Project(TWRP) and CMR(CyanogenMod Recovery)
Development Ceased: ClockWorkMod Recovery(CWM or CWMR) and PhilZ Touch