Fandom Category: The Avengers/Captain America
Pairing: Peggy Carter/Steve Rogers
Fic Title: Mono (the Super-Soldier Serum Strand)
Genre: fix-it fic
Why This Must Be Read: From the title and the summary - which makes it clear Peggy has become immortal by kissing Steve - I thought this story was going to be pure crack. It is not. It's actually totally serious and not once does the absurdity of the premise hurt the issues dealt with here; namely immortality and what it means to face a never-ending future as well as the lies necessary to live that kind of life. Don't get me wrong, it's fun too. Peggy doesn't let immortality stop her from living. Her journey through the twentieth century is true to character and ties itself very nicely into canon. She meets several familiar faces from The Avengers film over the years but it never feels like the author is imposing or forcing Peggy into places she doesn't belong.
The above fic was originally written as a oneshot but now has several follow-up stories. None are necessary reading (though I wholeheartedly recommend them all, particularly "In My Coffin..."), however one stands perfectly fine on its own and I just had to give it its own recommendation below.
Fandom Category: The Avengers
Pairing: Natasha Romanoff/Clint Barton
Fic Title: Keep Marrying You ('Til I Fall in Love)
Genre: five times
Why This Must Be Read: This is just what it sounds like. Clint and Natasha get married several times on various missions and fall in love along the way. This is a couple it's easy to under- or over-do but this fic handles them beautifully. We get to see them grow closer from their initial meeting all the way to their final wedding, but they never stop being them in favor of fluff. Not that there isn't fluff, it's five times they got married after all. Several of the circumstances, while believable, are hilarious.
Also, if you're worried about reading this without reading the rest of the series, don't be. There's only one minor reference to "Mono" and since you already know Peggy's alive, it won't be that much of a surprise.