I remember first hearing New Pornographers and The National on episodes of Chuck. As others have said Chuck always had good music choices.
There's also an episode of Veronica Mars that I recall using The Format
Yep, On Your Porch during a Veronica/Duncan scene.
La Rocca - Non-believer on One Tree Hill.
The show may have been absolutely ridiculous but damn they knew how to choose music.
I'll never forget Finch's What it is to Burn in the pilot, during Nathan and Lucas's basketball game at the end. That was the first time I heard Finch then went to listen to that album.
Since The National has been brought up several times, Friday Night Lights has several scenes where they used The National and it was so good, one of which was changed on the dvd and it upsets me. And Game of Thrones had a great ending with The National doing the Lannister song.