His web-shooters are mechanical devices filled with a fluid of his invention, the stupid stingers are gone, he can't communicate with spiders etc.
WTF? Talking to spiders? Who comes up with this shit? Who does he think he is Aquaman?
During JMS' run Spider-Man received a few power upgrades. However, IIRC, it wasn't actually JMS who wrote them in.
While Avengers Disassembled was going on, a tie-in in Spectacular Spider-Man (I forget who wrote it) enhanced his strength and Spider-Sense and gave him organic webshooters.
In Spider-Man: The Other (mostly written by Peter David, again IIRC) which crossed over between Amazing, Spectacular and Friendly Neighbourhood, he gained enhanced Spider-Sense which allowed him to use spiders as a kind of proxy, he would sense what they were sensing.
For instance, he was able to find a little girl in a collapsing building by creating a large web and then using his Spider-Sense to feel vibrations in that web.
He also gained bone stingers that would appear much like Wolverine's claws from his wrists.
As a direct result of The Other, he and Tony Stark became better friends and Stark constructed the "Iron Spider
" costume/armour. That costume gave him limited gliding ability and various electronic abilities (emergency service tracking etc).
This costume became important in the build up to the Civil War. It seems that the costume was recording data on Spider-Man's Spider-Sense. Stark was able to replicate it within his own armour to a limited degree and, when Spidey switched sides, was able to nullify it. Stark also created an override that would cause the suit to shut down. Unfortunately for him, he failed to realise that Peter is a very
smart guy and had changed the password on the override after figuring out it was there.
All of this has been undone by Brand New Day, however the Initiative operatives known as the Scarlet Spiders still wear copies of Iron Spider armour.