駆けっこ
かけっこ (foot) race

駆けつける
かけつける to run to to come running to rush (someplace) to hasten

駆ける
かける to run (race, esp. horse) to gallop to canter

駆け上る
かけあがる to run up

駆け下りる
かけおりる to run down

駆け下る
かけくだる to run down

駆け付ける
かけつける to run to to come running to rush (someplace) to hasten

駆け付け三杯
かけつけさんばい three cups of sake which latecomers to a party are made to drink

駆け出し
かけだし novice beginner

駆け出す
かけだす to run off to break into a run to start running

駆け回る
かけまわる to run around to bustle about

駆け寄る
かけよる to rush over to run up to

駆け巡る
かけめぐる to run about

駆け引き
かけひき bargaining haggling tactics strategy

駆け抜ける
かけぬける to run past from behind to run through (e.g. gate)

駆け登る
かけのぼる to run (uphill)

駆け落ち
かけおち defeat and flight disappearing without a trace eloping

駆け足
かけあし running fast double time

駆け込み
かけこみ last-minute rush stampede

駆け込み寺
かけこみでら (women's) refuge

駆け込む
かけこむ to rush in (at the last minute) to stampede