Importance is not always a measure of quality. So keeping that in mind.
1)
USM #1-6 - Bendis' starts out at Marvel, and Ultimate Marvel is born of the success of USM, the most influential Spider-Man story of the 21st Century. Far more than Lee-Ditko-Romita, USM has overwritten the idea of Peter Parker as a teenager and justified Marvel's
thought-destroying cliche of it being about youth. It did this for better and for worse.
2)
OMD - The worst Spider-Man story of all time is also the most important Spider-Man story of the 21st Century as far as 616 goes. Far more important than any story that came after that in BND, Slott, or Spencer's run.
3)
The 9/11 Issue, aka ASM #36 V2. The most important event of the 2000s was marked a few months later in this comic which was spread and disseminated widely among many survivors, children, and people as an outlet of grief. Even if it's probably not canonical (and not intended to be) this is still a good example of a major comics publisher making a response to a major world-historical event, and it deserves to be ranked among earlier comics that responded to World War II and Vietnam. IT is also far more humane, responsible and compassionate than drivel like Holy Terror.
4)
The Pulse #1-5, saw Norman Osborn being imprisoned for the first time in his 40-Year Publication history. It happened in a team-up story with Spider-Man, Luke Cage, and Jessica Jones, setting the stage for Bendis' New Avengers (which came out a few months later, and heavily featured all three characters and later issues of the Pulse was a tie-in to NAv) and for Osborn eventually becoming a Marvel-Wide villain in Dark Reign.
5)
CIVIL WAR - Another bad comic that is far more influential and important than good. The tie-in issues with JMS are better though, albeit more important for Captain America (who got his big "You move" speech in ASM).
6)
JMS' The Conversation, ASM #37 V2 - This single comic drastically changed Aunt May and inspired Bendis' own attempt to have Aunt May learn the secret in USM and Kevin Feige's take on May in Homecoming and FFH. Aunt May was never the same after this, and after JMS, no other comics writer has written a decent story with her.
7)
Marvel Knights Spider-Man - Mark Millar's 12 issue run was a major influence on Greg Weisman's
The Spectacular Spider-Man inspiring the characterisation of Norman Osborn in that story, while also borrowing the serialized blend which merged all the Spidey rogues with each other and the subtext of CEO creating supervillains to keep Spider-Man occupied from going after corporate crime.
8)
Spider-Man Loves Mary Jane - Sean McKeever's teen centered shonen-style take on Spider-Man in high school was a big inspiration for Jon Watts and his MCU movies. It also highlighted the use of AU and its importance in the world of Spider-Man.
9)
JMS' Coming Home ASM #30-35 V2 - The fight with Morlun and the establishment of the Spider-Totem were magical realist intrusions to the Spider-Mythos (heck the first time we thought that Spider-man had a mythos) and set the stage for the Spider-Verse sub-franchise.
10)
To Have and to Hold Sensation Spider-Man Annual #1 - This was Matt Fraction's first major work at Marvel and as per him, it was this comic, his collaboration with Salvador Larocca that got him the gig to work on Iron Man, and later go on to further success with Hawkeye. It's also an enduring classic romance story, with multiple issues after it alluding to imagery from this story.