競べ[kurabe] contest
駅伝競走[ekidenkyousou] long-distance relay race
価格競争[kakakukyousou] price competition
競う[kisou] to compete with
競る[seru] to compete

競泳[kyouei] swimming race
競演[kyouen] recital contest
競技[kyougi] game
競技者[kyougisha] competitor
競合[kyougou] contention

駈ける[kakeru] to run (race, esp. horse)
駈降りる[kakeoriru] to run down (stairs, etc.)
駈足[kakeashi] running fast
駈落ち[kakeochi] defeat and flight
駈出す[kakedasu] to run off

駈引[kakehiki] bargaining
駈け出し[kakedashi] novice
牧を駈ける駒[makiwokakerukoma] horse galloping in the pasture
駈歩[kuho] canter (horse gait)
駈けっ競[kakekkura] (foot) race