Personnally, I like to know the song of birds that can likely be seen around here someday. A couple of years ago, a hawk was hunting around our feeders. I called it a sharp-shinned because it's the one normally seen around. When it started screaming after the jays, I realized it was a Cooper's. To find the right species it was important to know both song.
The same thing happened with Clay-colored sparrow. I already knew its song before I found it for the first time.
So for that same reason, I learned the following song to make sure I don't miss a single bird if I can ear it someday:
Yellow-billed cuckoo, Willow flycatcher, Carolina wren, Wood trush, Golden-winged warbler, Yellow-throated vireo, Eastern towee, Henslow, Field, Nelson's, Grasshopper sparrows.
However, it's way more important to learn about our common species. If somebody knows the common songs pretty well, he's gonna be able to know when he ears a song for the first time. That's the first step to identify uncommon species: to know our limit, and be comfortable with what we already know. EG: If your in an Alder flycatcher habitat and you ear a song, you have to already know the Alder flycatcher song pretty well to know that what you ear is different.
Can't wait for the spring!