M_Ryuuji from animelyrics said:
込む (komu), "in", as in 飛び込む (tobikomu/jump in), 書き込む (kakikomu/write in/post) (Note that the noun 書き込み/kakikomi is usually used for a message board "post")
出す (dasu) "out" or "off," as in 駆け出す (kakedasu/run off), 歩き出す (arukidasu/walk out)
合う (au) "together", "each other" - as in 話し合う (hanashiau/talk to each other), 響き合う (hibikiau/echo each other)
合わせる (awaseru) "combine", "bring together" - such as 組み合わせる (kumiawasu/to join together)
上がる (agaru) "up" - as in 飛び上がる (tobiagaru/jump up) or 燃え上がる (moeagaru/burn up)
下ろす (orosu) "down" or "over" - 見下ろす (miorosu/to look over/look down on)
下げる same as 下ろす but with a greater feeling of physical force, 引き下げる (hikisageru/pull down)
入れる (ireru) "into", as in 運び入れる (hakobiireru/carry into) 取り入れる (toriireru/take into/absorb)
落ちる (ochiru) "down" (in a falling sense), as in 焼け落ちる (yakeochiru, burn down) 滑り落ちる （suberiochiru/slip down/fall down)
返す (kaesu) "back" - as in 取り返す (torikaesu/take back), 殴り返す (nagurikaesu/hit back)
通る (tooru) "through" or "past" with an emphasis on the state in between - as in 突き通る (tsukitooru/push through/penetrate)
抜く (nuku) "through" or "past" with an emphasis on the state after - as in 走り抜く (hashirinuku/to run through/past), 追い抜く (oinuku/to pass/outdistance)
続ける (tsudukeru) "continue" - as in 話し続ける (hanashitsudukeru/keep talking)
進む (susumu) - as in 書き進む (kakisusumu/keep on writing) (similar to 続ける)
終わる (owaru) "stop" - as in 読み終わる (yomiowaru/finish reading)
超える (koeru) "over" or "past" - as in 飛び越える (tobikoeru/jump over)
付ける (tsukeru) "on" with a feeling of attachment, like 受け付ける (uketsukeru/to recieve and keep)
消す (kesu) "away" or "gone" - as in 打ち消す (uchikesu/to push away/to deny), or 取り消す (torikesu/take away/cancel)
比べる (kuraberu) "compare" - as in 食べ比べる (tabekuraberu/eat and compare)
きる (kiru) "completely" or "totally" - as in なりきる (narikiru/to completely become), or 読みきる (yomikiru/to completely read through)
過ごす (sugosu) "over ____" - 見過ごす (misugosu/overlook/let slide)