For the existence of the Arizona Cardinals and the years of putrid football, they have never held the top selection in any NFL Draft.
In a number of different seasons, they have come close.
In 1998 they picked second and missed on Peyton Manning (they ended up avoiding the costly error of taking Ryan Leaf, traded down to three and had one of the best trade hauls in NFL Draft history).
In 2001, they picked second and missed on Michael Vick. They settled for Leonard Davis who was miscast as a tackle, before moving onto Dallas to become an Pro Bowl guard.