In looking at the history of the players who have been chosen last in the NFL draft, aka Mr. Irrelevant, a number of them have played with some success, and primarily they have been receivers and linemen. Only one has made the pro bowl. To see who, hit the jump.
As seen in the above link, the only pro bowler chosen with the last pick was place kicker Rolph Benirschke. Typically teams don't draft kickers, primarily I think, because they know there will be enough available as UFA to get someone decent. But with the last pick, why not choose who you would most like to sign, and then acquire exclusive rights to him via the draft? And here I am actually thinking about acquiring a punter rather than a place kicker. A couple of possibilities would be Derek Epperson from Baylor who averaged 44.2 and 44.8 over the last two seasons, and Rob Long (don't you love the name for a kicker?) from Syracuse who averaged 43.9 and 43.6 the last two years. Who would you nominate for this pick?