I'm in agreement with @Grey on some things and @Doc on others..
I think all Spider characters should be at the top in terms of: Agility, Acrobatics, Flexibility, Gymnastics..and anything else of the sort. Even if they haven't had any formal training, the level of their superhuman prowess allows them to be above all others without needing such.
So Spiders are #1..
#2 Beast. I find it that no one else besides the Spiders can top him, and even with some of the Spider characters it's highly debatable that they top him.
#3 I'll give this to Nightcrawler aswell. To me he's always shown to be a near equal to Beast. To me he's a fair middle ground between Characters like Beast, and those like Panther.
#4 Black Panther. He's regularly shown to be more nimble and agile than others in his class, such as: Captain America, Winter Solider, Wolverine, Blade, Moon Knight, Deadpool, Kazar, etc. Yet because they are all relatively equal physically, being fair, I'd say they also for the most part can copy each others Acrobatic feats- and thus share an equal level of agility or acrobatic prowess; each just applies such differently. Panther to me seems as the one between them all who relies on it more, and incorporates such more with his animalistic jungle style. Such is why, in my opinion, he's the "spokesman" for this level of superhuman physicality when it comes to this topic.
#5 Daredevil. Matt represents the true street level peak human characters of Marvel in my opinion. With no enhancements, and above all Olympic Level athletes, Matt has consistently shown to be very nimble, agile, and flexible, more than any other character in his class: Batroc, Elektra, Black Widow, Gambit, Shang Chi, Iron Fist, and more of the sort I feel are all in his class on this topic...but he is the top, in my opinion.
Overall my numbering more so represents a level, and Ive chosen specific characters that I feel represent that level or category the best.