What are yours? Here's my list, with a short explanation about why each strikes me as special. A few popular favorites aren't on my list -- your mileage may vary.
And I Love Her. A simple, straightforward love song with what's arguably the first of those lovely, bittersweet, slightly mysterious melodies that lifts the song to a whole new level and that would become a Paul trademark.
Here, There and Everywhere. Paul in dreamy-romantic mode. Pretty close to perfect.
I Will. Another dreamy-romantic tune, but with an odd twist in the lyrics that suggests the object of his affection may not even be real.
Maybe I'm Amazed. I don't know another song that so perfectly captures the beautiful but slightly scary nature of falling in love -- scary because it inherently involves surrendering control. The vocal takes what's suggested in the lyrics and brings it to electrifying life. My candidate for best rock love song (and best rock vocal performance) ever.
Every Night. If those "oohs" don't melt you, you may be made of granite.
I'm Carrying. Another emotionally complex, bittersweet tune. He's trying to patch something up that clearly went awry, and we don't really know how it will turn out.
My Valentine. This has always sounded to me like a long-lost George and Ira Gershwin tune. I love how the music tracks the mood in the lyrics, from pensive to joyous. A neglected masterpiece.
Hand In Hand. This one puzzled me at first: A love song with a melody that feels downright mournful. Then it struck me that the lyrics repeatedly raise the possibility that they may screw it up: "I will try to make it happen," "We can make each other happy if we get it right," etc. This is a love song that could only be written by someone who's lived long enough to see all the ways relationships can go wrong. Haunting. Exquisite.