#4 The New Day

It is surprising to see that a faction as successful as The New Day hasn't even won once at the Grandest Stage of Them All. However, it is true. The trio's first WrestleMania appearance as a group was in 2015 at the show's 31st edition. They were a part of two matches at the event, both of which were kick-off bouts. They first came up short of winning the Tag Titles. After that, all three members tried their luck in the Andre the Giant Memorial Battle Royal, but to no avail.
The New Day then lost to The League of Nations at WrestleMania 32 and The Bludgeon Brothers at Wrestlemania 34. The trio didn't participate in a match at WrestleMania 33 due to being the event's hosts.
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Regardless, The New Day still went on to become one of the most successful factions with overly impressive merchandise sales and multiple tag title reigns, including the longest one.
An Interesting Fact: Big E and Xavier Woods have also lost all their WrestleMania matches before the formation of The New Day. Kofi Kingston, on the other hand, has only been able to grab a single win (at WrestleMania 27) at the Show of Shows.