We report time-series photometry for 55 variable stars located in the central part of the globular cluster M55. The sample includes 28 newly identified objects of which 13 are eclipsing binaries. Three of these are detached systems located in the turn-off region on the cluster color magnitude diagram. Two of them are proper motion (PM) members of M55 and are excellent candidates for a detailed follow-up study aimed at a determination of the cluster age and distance. Other detached binaries are located along the unevolved part of the cluster main sequence. Most of the variable stars are cluster blue straggler stars. This group includes 35 SX Phe stars, two contact binaries, and one semi-detached binary. V60 is a low mass, short period Algol with the less massive and cooler component filling its Roche lobe. The more massive component is an SX Phe variable star. The orbital period of V60 increases at a rate of dP/P = 3.0 x 10(-9). In addition to numerous variable blue stragglers we also report the detection of two red stragglers showing periodic variability. Both of these are PM members of M55. We note and discuss the observed paucity of contact binaries among unevolved main sequence stars in M55 and NGC 6752. This apparent paucity supports an evolution model in which the formation of contact binaries is triggered by stellar evolution at the main-sequence turn off.