Last offseason, it was Marlon Byrd and Scott Kazmir who headlined a group of minor-league free agents that were able to parlay a spring training invite into spots on Opening Day major-league rosters. Jedd Gyorko and Jose Fernandez, both top prospects without a single day of big-league service time, did the same.
While the odds are usually stacked against those who aren't already on the 40-man roster—only four teams currently have space on their 40-man rosters, according to MLBDepthCharts.com—adding non-roster players requires players already on the 40-man roster to be removed (either by being placed on waivers, placed on the 60-Day DL, traded or released).
Truthfully, every year it's quite common for at least one or two players from each team to win a job in the spring and have their contract purchased from the minors prior to the start of the regular season.
Here is one non-roster invitee from each of the 30 teams with the best shot to crack their respective team's Opening Day roster.