6. Wes Welker (2004)
Welker was a highly effective wide receiver and led the league in receiving yards on three occasions. But his career almost didn’t start. The San Diego Chargers picked him up after he went undrafted. But he only played a single game for the franchise before they released him (via Boston.com). He had the option of joining their practice squad but opted against it.

Instead, he accepted a deal with the Miami Dolphins. It took him time to find his feet as he played on special teams. But finally, he became one of their most important attacking talents. This resulted in a trade to the New England Patriots. Welker never won a Super Bowl with the Pats but he was a vibrant threat for a number of seasons.