Spectacular Spider-Man is the best all from storytelling and direction, it's also very strong in continuity, animation, and characterization.
Unlimited Spider-Man: I'm aware this gets a lot of flack, but I've watched it late last year and guys, it's one of the best shows. Sure the first episode is wonky, but it deserves more love than most people believe. Though I hate anthropomorphic boobs, and lady Vermin's affection of the Human Spider.
Spider-Man (1994): I never thought this was the definitive take on the character and his world in animation, it stood true to the comics in many ways, but it also took too many liberties for me to take it as an ideal take. Kingpin is too central and overpowered, Doc Ock is just a pawn of Kingpin starting with season 3, Green Goblin is betrayed, a lot of continuity dysfunction and plot threads left dangling....
It has the best combination of detailed art and sweet animation, at its best it has some of the best animation for TV.
Spider-Man (2003): It's an interesting take with some good qualities that deserve some love and attention, but it's not very consistent in displaying Spidey's abilities.
Both 80s cartoons. Love 'em dearly, but they are not good.
Season 1 of the 60s cartoon. Memes and funnies, lot of pleasure watching how creative Spidey is with his webbing in this one. A completely stupid show though.
Ultimate Spider-Man: Drake Bell's voice doesn't fit Spidey, his quip delivery is not that good, TEAM stuff is not Spidey-like, and many 4th wall cutaways drop the enjoyment I have of this show to a degree. I enjoy it, but it loses points.
Spider-Man (2017): Opens up with an obnoxious Spider-Man I want to punch a lot of times, and then he needs to be told how to stop a helicopter by pedestrian Gwen Stacy who was almost killed. just a second later with a smile on her face.
There have been ups and downs on the way, some of the ups show potential of greatness that is not fully realized but succeed in keeping me interested in the show, but shortly after it loses what made it more interesting.
Ralph Bakshi's Spider-Man: What is that? Seriously, what is that? It took a show and made a big mess going on a trajectory of its own with green skinned villains and recycled footage from other Bakshi shows.
I'm a child of the 90s, but to this day I will always take these two shows as the definitive take on Peter Parker in animation, and they presented us with two great and underrated Spidey voices in Dan Gilvezan (my personal favorite) and poor Ted Schwartz (even post mortem, hardly anyone thinks of him as a Spidey voice).