S.H.I.E.L.D. also appeared first in this issue, which was written by Stan Lee and drawn by Jack Kirby...but Hydra has a history both before that issue (in a stand alone tale in Atlas Comics' Menace #10 (March, 1954) where it was only a reference to an organization by a scientist in the tale "Half Man, Half...?" with art by Robert Q. Sale...but it was only a mention, and Stan and Jack created the green and yellow uniforms and the philosophy of the group...
...still, you can see the reach of Hydra extends even past its own beginnings!
Hydra vs. S.H.I.E.L.D.
The team then went to Nick Fury, Agent of S.H.I.E.L.D. for 18 issues from June, 1968 to March, 1971.
All these tales can be found in Marvel Masterworks:Nick Fury, Agent of S.H.I.E.L.D. #1 has Strange Tales #135-153 (and Tales of Suspense #78 and Fantastic Four #21 which relate, and Tales of Suspense features stories on A.I.M. as well, which is a branch of Hydra at the time and Nick fighting them with Captain America, and the Fantastic Four story is a pre-S.H.I.E.L.D. appearance which brought Nick Fury from World War II to "modern times" and they faced the Hate-Monger).
Marvel Masterworks:Nick Fury, Agent of S.H.I.E.L.D. #3 has the stories from Nick Fury, Agent of S.H.I.E.L.D. #4-15, Avengers #72 and Marvel Spotlight #31 (Nick Fury, Agent of S.H.I.E.L.D. #16-18 were reprints of Hydra battles from Strange Tales) and finishes Nick's battle against Scorpio as well as another battle with the Hate-Monger.
Still, this didn't end the Marvel Universe's battles with the forces of Hydra, as their coda implied...they came back else where many times. A few of their other more important appearances include...
Hydra vs. Captain America
Hydra vs. the Hulk
Hydra faced the Hulk in the Incredible Hulk #132 (October, 1970) in a story by Roy Thomas with art by Herb Trimpe and John Severin, wherein the evil organization convinced Hulk's helper, Jim Wilson, into trying to capture the Hulk.
It didn't work out so well for Hydra (and they tried to attack him again in Incredible Hulk #154, August, 1972 by Archie Goodwin and Herb Trimpe, with the help of Spider-Man foe, the Chameleon, shrinking the Hulk, who got some help himself from Hank Pym....the Ant-Man!). Oddly, Hulk usually spent more time fighting the army (with General Thunderbolt Ross and Major Glenn Talbot) or S.H.I.E.L.D. itself than Hydra...
Hydra vs. Captain America II
Hydra vs. the monsters
As Tigra, Greer helped defeat this group of Hydra with the help of the Werewolf by Night, Jack Russell in Giant-Size Creatures #1 (July, 1974, by Tony Isabella and Don Perlin). Tigra had a brief solo feature in Marvel Chillers #3-7, and worked with Spider-Man, the Thing and the rest of the Fantastic Four here and there, and eventually joined the Avengers (briefly on the east coast, and was a founder of the West Coast Avengers offshoot).
Hydra vs. Daredevil and Black Widow
Another Supreme Hydra is revealed (...yet another Spider-Man crimelord, different from the previous one mentioned earlier), as well as a few other villains (Daredevil foes like el Jaguar and Blackwing, and Spider-Man/Cat foe the Man-Killer from the Cat's last appearance in Marvel Team-Up #8 were revealed to be Hydra agents, connecting a few disconnected storylines....).
Hydra vs. the Thing and Shang-Chi
Hydra vs. the Invaders
In a group led by Baron Strucker (a Nazi foe of Sgt. Fury's who first appeared in Sgt. Fury #5 in January, 1964) in Marvel Universe #1-3 (June-August 1998 by Roger Stern and Steve Epting), Hydra faced the World War II superheroes the Invaders (Captain America, the android Human Torch, Namor the Sub-Mariner and the Whizzer) as well as detailing a little of Hydra and the baron's past (like his battle with Captain Savage and his Leatherneck Raiders in Captain Savage #2-4, March-July, 1968).
Hydra did indeed have a history stretching back to World War II!
Hydra vs Sub-Mariner
Hope you enjoyed Hydra's greatest hits, and the how the heroes of the Marvel Universe hit them back!