My all time main squeeze (that's right, it's a player no longer with the organization, how old school) for the duration of the team's current incarnation would have to be the extremely useful Mike Stanton.
The always left handed Texan managed to acquit himself quite nicely as a pitcher for America's Team in 2005 (and I'm sure he enjoyed the dimensions of RFK if not the food). And then, in late September of that same year he was traded to the Red Sox for two prospects, parting ways amicably with the team and netting it two players with at the very least a minimal amount of potential.
After playing out his contract in Boston, he returned to Washington the next year, where he was again traded mid-season for young talent, this time to the Giants. And so, after two years and very little money expended, the Nationals were the recipient of roughly seventy innings of respectable work on the mound and three players to help revive its very nearly lifeless minor league system. The Nationals did twice associate upon the baseball diamond with Mike Stanton, and their joining was most fruitful.
Conceivably we could continue to sign this man and trade him away for youth until our entire organization was the product of a contender's need for a second lefty heading into the playoffs.
My second fave, again counting all players who've played on the team during its time in the District, would be Livan Hernandez. There's very little more entertaining in the game of baseball than watching that man pitch when he's right. Completely whiffing on one of his very slow curves must rank up there with being late on a Jamie Moyer fastball and not hitting a home run off of Eric Milton as one of the most embarrassing things players can do with bats in their hands.
My favorite current national would probably be Nick Johnson if I didn't in my weaker moments sometimes think he really could do something to stop getting hurt so damn frequently. His fragility being what it is I've been making doe eyes at Chad Cordero, I do appreciate how conscious he is of the fact that he's uniquely capable of challenging hitters to wail on a high fastball and still retire them, pitching where he does, and how consistently he manages to pull off that stunt.