Tapping out is seen as a massive personal failing in the kayfabe world of WWE, even though - in real life - admitting that you have a normal human pain threshold is clearly preferable to getting your arm snapped like a twig because you were too proud to quit.
Despite this, most of the company's top stars have, at one point or another, been made to submit. Triple H tapped at WrestleMania XX. Brock Lesnar gave up at SummerSlam 2003. Even John Cena, the walking embodiment of wrestling's never say die spirit, was forced to break the habit of lifetime during his early days by Kurt Angle.
While each of the aforementioned are guilty of bringing shame upon their families, a handful of others have managed to avoid this fate, going the entirety of their WWE career (at least, so far) without once giving up like a little baby.
Note: the case of The Undertaker is a slightly dubious one, since most of the times he has "tapped out" there have been mitigating circumstances (for example, Teddy Long recreating the Screwjob at Breaking Point '09). On the basis that he has been beaten via submission, we're going to exclude him from the list.