Players non-tendered a contract automatically become free agents, although they are not excluded from re-signing with their former team.
Among notable players who were non-tendered were Nationals' LHP John Lannan, LHP Tom Gorzelanny, C Jesus Flores, Giants' RHP Brian Wilson, Braves' RHP Jair Jurrjens, RHP Peter Moylan, Orioles 3B Mark Reynolds, Rangers' C Geovanny Soto, and Red Sox RHP Scott Atchison.
Usually, players become non-tendered because their former teams don't want to give them an overvalued contract through arbitration. Such was the case with the Mets and Mike Pelfrey. They have both reportedly expressed mutual interest in a reunion (under the right conditions), but the Mets clearly didn't want to pay Pelfrey in excess of $6 million he would have earned through arbitration coming off of Tommy John Surgery. The difference now is these players are free to negotiate with other teams.
Among the names worth watching are Lannan, Flores, Soto, and Atchison.
Flores (who was originally signed by the Mets in 2002 but was taken by the Nationals in the 2006 Rule 5 draft) was displaced by Kurt Suzuki at the trade deadline this past season. He has never played more than 90 games in a season but he's a strong defender and knows the National League East, given his years with the Nationals.
I wouldn't expect the Mets to have Soto at the top of their list this winter. In fact, I'd prefer they go after Kelly Shoppach and Miguel Olivo in that order before even figuring out where Soto is on their board. He does hit for power but not much else and he's been an inconsistent defenseman for most of his career. It's amazing how far his stock has fallen since he won the Rookie of the Year Award in 2008.
In regards to Lannan, the Mets could be interested in him if they end up dealing either R.A. Dickey or Jon Niese for a position player. Lannan lost his job with Washington last Spring after they acquired both Gio Gonzalez and Edwin Jackson. At that time, I thought the Nationals might move Lannan, but they sent him to the Minor Leagues instead where he spent most of his season. He doesn't throw hard and relies primarily on a fastball and sinker for his primary pitches. But he has always been a solid and durable back-of-the-rotation pitcher, and if a need develops, Lannan can be a low cost solution while they wait for Zack Wheeler to be ready.
In regards to Atchison, he could end up being a find for any team who signs him. He's always been a solid piece of the Red Sox bullpen. He doesn't throw hard and he owned left-handed hitters in 2012, holding them to a .188 average. That's not indicative of his career numbers, but he always throws strikes and keeps the ball in the ballpark. Depending on what the Mets do with their bullpen, Atchison could be a good, under-the-radar acquisition for them as they search for a veteran presence.
Lastly, a lot of people asked me about Brian Wilson last night. He is coming off Tommy John Surgery and missed most of the 2012 season, but he should be ready in the early part of the 2013 season. He is a colorful personality and was outstanding in his years with the Giants, and I think he will be productive when he comes back. If he had gone to arbitration with the Giants, he would have likely earned between $8-9 million (which is why the Giants non-tendered him). He is reportedly considering both the Dodgers and Red Sox now that he is a free agent. Wilson will still be pricey in free agency and given their other priorities and recent history with overspending for bullpen help, I don't see the Mets bidding for his services.
Per MLB rules, a player cannot earn less than 80 percent of his prior year's salary through arbitration. A player is arbitration eligible three times unless he earns "Super Two" status (a player who has two years of service but less than three years, based on a determined figure by MLB at the end of each season) in which case he is eligible four times, after which he can become a free agent.