Steve Hands for OHM commented "Run" is "the kind of rueful facing-up-to-life type anthem" and added it is a "decent stab" for radio stations like XFM and Virgin Radio, a reviewer of Contactmusic.com called it "shimmering", and Dom Gourlay of Drowned in Sound gave the song a rating of 8/10. Virgin Music listed "Run" 8 in their list of "Top pub sing-along anthems". It appeared at number 874 of "The Rock 1000" list of "best rock songs of all time", published by New Zealander radio station The Rock FM. Emma Taylor and Lorelei Sharkey, Em & Lo, listed "Run" at number 69 of their "Top 100 Breakup Songs of All Time", in their book "The Ultimate Guide to Dumping and Getting Dumped". Along with the song "Same", "Run" is one of the favourite Snow Patrol songs of American heavy metal band Mötley Crüe member Tommy Lee.