When Captain America was killed by the Red Skull and Crossbones after Marvel's Civil War event, the recently returned Winter Soldier, aka Bucky Barnes, picked up the shield and became Captain America. He had no experience in being a public leader and symbol like Steve Rogers, but Bucky still took on the challenge. He soon joined up with the fugitive New Avengers and helped them fight the Initiative, the Skrulls, and Norman Osborn's Dark Reign.
While Bucky tried his best to be the Captain America the Marvel Universe needed at the time, he wasn't ready for the responsibility that comes with the symbol. He did plenty of good, but he also made mistakes.
10 BEST: Picking Up The Mantle
While one could argue whether or not Bucky was qualified to become Captain America in the first place, it's undeniable that the Marvel Universe needs a Captain America. Cap is one of those few mantles that has ascended to the level of symbol, both in and outside the actual comics canon. There were a few people who were considered for the shield, including Clint Barton, but Bucky stepped up and took up the shield and the title of Captain America.
9 WORST: Not Beating The Tar Out Of Tony Stark
Iron Man was a part of the hunt for a new Captain America and agreed that Bucky was a good choice, but that doesn't change the fact that Tony was still on his pseudo-fascist kick from Civil War. He was still leading the Initiative and hunting down unregistered superhumans across the United States. He was still hunting Luke Cage's New Avengers, and Bucky would have been more than justified in slugging Tony Stark a few times for his part in all of it. Thor did when he made his return around this time.
8 BEST: Going Underground
That said, Bucky did make the right choice in not joining with Iron Man and the Initiative and, instead, going underground and joining up with the Luke Cage's New Avengers team. He recognized that it's what Steve would have done, as Cap led these heroes during Civil War. Bucky made the right call here, and he helped the New Avengers stay ahead of Norman Osborn's Dark Avengers.
7 WORST: Not Dealing With Osborn
While Bucky is far from the only one guilty of inaction here, he still holds a certain degree of guilt here. The weird hitch of Dark Reign is the fact that nobody seemed to be dealing with Osborn's more aggressive and open form of fascism when he led the Dark Avengers and H.A.M.M.E.R. Everyone seemed to just shrug their shoulders.
The New Avengers fought them from underground to a point, but they never seemed to make any open and public calls to shut it all down. Bucky as Captain America could have been an especially powerful asset here, as Cap was still a symbol people could rally around. Clint Barton, then Ronin, may have been the most proactive against Osborn, as Clint tried to assassinate Norman.
6 BEST: Saving Toro's Body
Toro, the sidekick of the original Human Torch, is a character whose life and death seem to ebb and flow in Marvel Comics, but he was definitively dead by the time that Bucky became Captain America--at least for a while. The Man With No Face and other malefactors sought to take and experiment on the body of Toro. Bucky, Falcon, Namor, and Black Widow fought to keep Toro out of their hands. It was an honorable move on the part of Bucky, and it helped preserve the memory of a fallen friend--who would be resurrected by Bucky himself not too long after.
5 WORST: Falling Into Baron Zemo's Trap
While it's debatable how much Bucky could have done to avoid this, it did feel like Bucky Cap fell face-first into Baron Helmut Zemo's attempts to expose his past as the Winter Soldier. Zemo even told Bucky that he was going to do this, but Bucky was still exposed and came under fire from both the United States and Russian governments. This landed Buck in a Russian Gulag and almost killed by Ursa Major of the Winter Guard.
4 BEST: Trying To Help The 1950's Cap
William Burnside filled in as Captain America when Steve Rogers and Bucky Barnes were seemingly killed by Baron Zemo's missile. He was mainly active during the 1950's, but his version of the Super Soldier Serum allowed him to live through to the present day...but it also left him mentally unstable.
The Watchdogs, a reactionary militant group, recruited Burnside to their cause and led him on a rampage to return things to the "real America." Bucky intervened and tried to help Burnside, but, unfortunately, the former Captain America was too far gone. It ended with Bucky shooting Burnside, and he fell off a dam. Miraculously, Burnside survived the experience and was later found by a revived Steve Rogers.
3 WORST: Failing To Lead The New Avengers
Bucky Barnes, for all his qualities, is not much of a leader, and this came through when he joined the underground New Avengers after Secret Invasion. Luke Cage led this New Avengers team and did so with aplomb, but Captain America needs to be a figurehead. Bucky couldn't quite live up to the task and fell into the background behind Luke. He was still a good team player, but he could have done more for the New Avengers.
2 BEST: Leading The Charge At Central Park
Despite that, Bucky did take charge at the Battle of Central Park during Secret Invasion. This battle against the Skrulls saw the return of both Captain America and Thor, and they, along with Iron Man, led the New Avengers, Mighty Avengers, the Secret Warriors, the Fantastic Four, and the Thunderbolts against the Skrulls. Here, Bucky lived up to the Captain America name and helped free the world of the Skrull occupation.
1 WORST: Not Coming Forth With His Past
This mistake ended up being Bucky's downfall as Captain America, and it made Baron Zemo's job all the easier. Bucky never came forward with his past as the Winter Soldier, and he didn't take any steps to do so. As such, Baron Zemo was able to leave breadcrumbs that led to Bucky's exposure as the Winter Soldier, and it led him to the aforementioned Russian gulag. He later escaped and joined the Avengers in their fight against Cul, the Asgardian God of Fear and Sin, Daughter of the Red Skull. The latter led a new Blitzkrieg against America while armed with an enchanted Asgardian hammer gifted by Cul, and she seemingly killed Bucky in battle. Thankfully, Bucky barely survived, and he went back to working as the Winter Soldier--but this time on the side of the heroes.