The 1960s Captain America Adventures

Having successfully introduced a new Human Torch, and reintroduced the Sub-Mariner, Marvel tried reviving Captain America.  As a test, they had the Human Torch fight an acrobat dressed as Cap, then asked the readers to write in if they'd like to see the real Cap return.  Apparently, the readers would, as Marvel brought back the original Cap in the pages of The Avengers, claiming he had been frozen in ice for 20 years (and conveniently ignoring the post-war adventures of Cap).  Cap joined the Avengers, but soon got his own series in half of the Tales of Suspense title (the other half going to Iron Man).

If you want micros of any villains Cap fought while with the Avengers, you should visit Robert Bradley's excellent Avengers MicroHeroes site, Avengers Assemble!  Here, I'll cover only the foes he faced in his modern-day adventures in his own series.
Boss Bull's Mob Captain America
The Assassins
Baron Zemo
The Army of Assassins Strikes!
Sumo The Strength of the Sumo!
Deacon Break-Out in Cell Block 10!
the First Sleeper The Sleeper Shall Awake!
Von Kimmer The Sleeper Shall Awake!
Erica Wolfmann The Sleeper Shall Awake!
the Second Sleeper
Schlag/Agent Three
Where Walks the Sleeper!
Third Sleeper The Final Sleep
30 Minutes to Live!
Sharon Carter The Gladiator, the Girl, and the Glory
Peggy Carter If a Hostage Should Die!
"Them" Them!
Red Skull
The Red Skull Lives!
the Cosmic Cube He Who Holds the Cosmic Cube

The Red Skull Supreme
Adaptoid The Maddening Mystery of the Inconceivable Adaptoid!
Tumbler Enter ... the Tumbler
Super-Adaptoid The Super-Adaptoid!
Hydra The Blitzkrieg of Batroc
General Li Chou The Secret
Planner Wanted: Captain America!
Power Man If Bucky Lives..!
Swordsman Back From the Dead!
...And Men Shall Call Him Traitor!
The Last Defeat!
Before My Eyes, Nick Fury Died!
Modok Into the Jaws of ... A.I.M.
If This Be... Modok
"Gunner" Gates A Time to Die -- A Time to Live!
Sniper To Be Reborn!
"Irma Kruhl" And So It Begins--!
Black Panther The Claws of the Panther!
Zemo impostor The Man Who Lived Twice!
This Monster Unmasked!
the Fourth Sleeper When Wakes the Sleeper!
The Sleeper Strikes!
Iron-Hand Hauptmann
The Weakest Link!
Slave of the Skull!
Living Laser In the Name of Batroc!
Cyril Lucas Cap Goes Wild!
Doctor Faustus If the Past Be Not Dead
Trapster The Snares of the Trapster!
The Hero that Was!
Hulk No Longer Alone!
Madame Hydra No Longer Alone!
Tomorrow You Live, Tonight I Die
Lest We Forget!
The Strange Death of Captain America
Stiletto The Man Behind the Mask!
Now Begins the Nightmare!
Far Worse Than Death!
Falcon The Coming of the Falcon
The Falcon Fights On
Now Falls the Skull!
Crack-Up on Campus!
Man-Brute The Coming of the Man-Brute!
Scorpion The Sting of the Scorpion!
Suprema, the Deadliest of the Species!
Cyborg Mission: Stop the Cyborg
Mandarin Captured in Viet Nam!
Diamond-Head The Fate of the Falcon!
The Maggia The Fate of the Falcon!
X-4 Who Calls Me Traitor?
Satan's Angels Mission: Stamp Out Satan's Angels
The Vengeance of the Red Skull
Hood Up Against the Wall
Whirlwind Up Against the Wall
Porcupine Up Against the Wall
Baron Strucker robot Bucky Reborn
Bucky robot Bucky Reborn
The Fearful Secret of Bucky Barnes
Bulldozer android Madness in the Slums
Stone-Face They Call Him Stone-Face
Doctor Gorbo More Monster than Man
Mole Man The World Below
Spider-Man To Stalk the Spider-Man!
It Happens In Harlem
Patrolman Steve Rogers The Badge and the Betrayal!
Grey Gargoyle In the Grip of the Gargoyle!
The Unholy Alliance!
And In The End...
The People's Militia Power to the People
Hydra Over All!
The Femme Force Mission: Destroy the Femme Force!
Kingpin And Behold the Hordes of Hydra
the Fifth Sleeper The Big Sleep!
Jakar All the Colors of Evil!
Mirror, Mirror!
Mister Hyde Panic on Park Avenue
Terror in the Night!
Captain America IV
Bucky II (IV?)
Captain America--Hero or Hoax?

The Falcon Fights Alone
The Incredible Origin of the Other Captain America!
Two Into One Won't Go!
Viper Veni, Vidi, Vici: Viper!
The Crime Wave Breaks!
Cowled Commander Turning Point!
Enter: Solarr!

If He Loseth His Soul!

This Way Lies Madness!
Beware of Serpents
The Werewolves
Queen of the Werewolves!
Yellow Claw The Yellow Claw Strikes
Night of the Lurking Dead
Ashes to Ashes
Phoenix II And a Phoenix Shall Arise!
Quentin Harderman When a Legend Dies
Moonstone J'Accuse
Banshee Believe It or Not: The Banshee!
The Secret Empire The Sins of the Secret Empire!
It's Always Darkest!
Number One
Number Two
...Before the Dawn!
Captain America Must Die!
Lucifer Lucifer Be Thy Name
If The Falcon Should Fall--!
Golden Archer Slings and Arrows!
Nomad The Coming of the Nomad!
The Mark of Madness!
Nomad: No More!
Cap's Back!
Scream the Scarlet Skull!
Mind Cage!
Druid The Madness Maze!
Alchemoid Druid-War