"Live and Let Die" (Paul McCartney & Wings)

Apart from the actual "James Bond Theme," "Live and Let Die" is the ultimate James Bond song.
It also, in my opinion, was James Paul McCartney's real return to form following the breakup of The Beatles.  (I don't count the cute-but-disposable single "Uncle Albert/Admiral Halsey."  Or, if we're talking album tracks, the highly overrated "Maybe I'm Repetitious Amazed.")  
To me, "Live and Let Die" captures both his penchant for balladry and ability to rock out like a madman when he feels so inclined.  The sentimental verses with their plaintive, cocktail lounge piano are the perfect foil for the crunch of Henry McCullough's guitar on the instrumental choruses.  And the brief bridge, which cleverly tosses in a little reggae flavor as a nod to the tropical setting of the film, provides a funky respite in the midst of the rock fire.
It is the perfect, dramatic opener for the only decent Bond film of the entire Roger Moore era.  (I mean, what the hell were they snorting when they made Moonraker?)
Story goes, ex-Beatles producer George Martin was asked to score the 1973 film Live and Let Die, so he offered the gig of writing the main theme to McCartney.  To get in composing mode, McCartney got a copy of the 1954 Ian Fleming paperback upon which the script was based, read it in an evening, and then wrote the song the next day.
In an article posted on the site of St. Louis radio station KHITS 96.3, there's a great quote from Wings drummer Denny Seiwell about how the song came together at McCartney's home studio.
"And we were up at the house one day, and he had just read the book the night before, and he sat down at the piano and said, 'James Bond...James Bond...da-da-dum!', and he started screwing around at the piano.  Within 10 minutes, he had that song written."
Just goes to prove what I've always suspected: McCartney can write some amazing music when faced with a challenge and/or has a fire under his ass.

"You Never Give Me Your Money" (The Beatles)

When it comes to The Beatles and songwriting, I've always been more of a John Lennon fan.  But it was never really a conscious "Lennon vs. Paul McCartney vs. George Harrison" kind of thing.  I just always liked the quirkier, snarkier, R&B-tinged numbers on my mom's Beatles records, and 90% of those songs just happened to be written primarily by Lennon.
McCartney's "You Never Give Me Your Money" from Abbey Road (1969) is one of a few exceptions, though.
If you're familiar with the album, you know the track is the starting point for the lengthy 8-song medley that comprises most of the album's second side.  But it's more than just a transition piece or bookend for the medley; it's a smart, funky mini-suite featuring one of McCartney's best-ever hooks that concisely summarizes the history of the Beatles up to that point.
Despite public perception that The Beatles were wealthy beyond belief, they actually were bleeding cash following the death of their original manager, Brian Epstein, in 1967.  So they brought on a new financial manager, Allen Klein—a hard-nosed American businessman who also managed The Rolling Stones in the 60s (and screwed Mick & Keef out of the rights to their back catalog).  McCartney wasn't a fan of Klein from the start and felt that his tactics were a little too smoke and mirrors.  
In short, the song opens with McCartney expressing his frustration with Klein always presenting them with vague financial statements on paper instead of actually showing them where the money was.  Hence the line: You never give me your money / You only give me your funny paper.
From there, he reminisces about "the good ol' days" when they were just getting started—no money, no obligations, and no managers, and then shuttles back to the present through a dizzying series of key changes, essentially thanking his new wife Linda for extricating him from the hell of business meetings and whisking him away to the countryside (Step on the gas and wipe that tear away).
Apart from it being a strong track lyrically, the song is one of the tightest final performances of the entire band together.  McCartney treats us to some damn fine boogie-woogie piano and his baritone "Elvis voice," à la "Lady Madonna," not to mention his inimitable melodic/rhythmic bass playing (especially on the 1-2-3-4-5-6-7 / All good children go to heaven coda).  But then there's also Lennon's raunchy distorted guitar, Harrison's bell-like guitar (fed through a rotating Leslie speaker), and Ringo Starr's simple but effective drumming, which punches and punctuates at all the right times.
Most bands don't sound this good when they're at the peak of their powers, much less when they're imploding.