The Cranberries blev internationalt berømte i 1990'erne med deres [[debutalbum]], ''[[Everybody Else Is Doing It, So Why Can't We?]]'', der blev en stor kommerciel succes. Gruppen har solgt over 40 millioner albums på verdensplan. De har haft fire top 20 albums på [[Billboard 200|''Billboard'' 200]] chart (''[[Everybody Else Is Doing It, So Why Can't We?]]''; ''[[No Need to Argue]]'', ''[[To the Faithful Departed]]'' og ''[[Bury the Hatchet (album)|Bury the Hatchet]]'')<ref name="US">{{cite web
 |url=http://www.billboard.com/bbcom/esearch/searchResult.jsp?configType=BBCOM_SIMPLEDEFAULT&pubList=Billboard&an=bbcom&action=Submit&kw=&exposeNavigation=true&keyword=The+Cranberries&submit.x=27&submit.y=14&submit=Submit&searchType=ARTICLE_SEARCH 
 |title=American Chart 
 |publisher=Billboard.com 
 |access-date=24. juni 2008 
 |archive-url=https://web.archive.org/web/20080801201840/http://www.billboard.com/bbcom/esearch/searchResult.jsp?configType=BBCOM_SIMPLEDEFAULT&pubList=Billboard&an=bbcom&action=Submit&kw=&exposeNavigation=true&keyword=The%2BCranberries&submit.x=27&submit.y=14&submit=Submit&searchType=ARTICLE_SEARCH 
 |archive-date=1. august 2008 
 |url-status=dead 
 |df= 
}}</ref> og otte top 20 singler på [[Alternative Songs|Modern Rock Tracks]] chart ("[[Linger (sang)|Linger]]", "[[Dreams (The Cranberries-sang)|Dreams]]", "[[Zombie (sang)|Zombie]]", "[[Ode to My Family]]", "[[Ridiculous Thoughts]]", "[[Salvation (The Cranberries-sang)|Salvation]]", "[[Free to Decide]]" og "[[Promises (The Cranberries-sang)|Promises]]").<ref name=US />
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