OK Handito off the top of my head:
First off, pocketman is right about Bernard Purdie and the half-time shuffle, the figure is generally considered his brainchild. The interesting thing is, and I'm pretty sure but not positive about this, Purdie's most famous use of it in a song (Babylon Sisters) was recorded after Fool In The Rain, but the influence for Fool in the Rain is definitely Purdie.
In several earlier versions of 'Moby Dick,' (Including Royal Albert Hall footage) Bonham starts the solo off with a figure where he plays a swing pattern on the snare and toms simultaneously that is a direct homage to Max Roach's 'The Drum also Waltzes.'
One book I read said that Bonham was very much into cream and Ginger Baker, and you can hear this was definitely an influence on his thunderous snare-bass-tom fills as Baker played similar patterns before him. Buddy Rich did at times too. I think Rich was Bonham's influence for drum sound. The tuning is very similar between the two. He credited the bass drum triplet inspiration to a Vanilla Fudge record, I believe a cover of the Beatles 'Ticket to Ride,' thinking that Carmine Appice was playing one bass drum when he was really playing two.
As far as Bonham's influence over other drummers, I really think it is so massive you could write a whole book about it. You can hear obvious influences in 70's-80's guys like Bobby Rondinelli, Cozy Powell, Nicko McBrain, and Frankie Banali up to more modern guys like Stephen Perkins, Danny Carey and Jon Theodore. I don't think it's an overstatement to say that 80 or 90% of rock drummers out there have taken something from his playing and would probably quote him as an influence.
His exact kit sizes are even being used more on stages. The guy from the Killers plays a Bonham set. So does the guy from the Black Crowes. So does Joey Castillo. So does Taylor Hawkins. Abe Laboriel Jr. plays a kit that has even bigger sizes but was probably Bonham influenced. If you look in a music catalog you'll find more kits with 24" and 26" bass drums then you ever would have 10 years ago. Those were mostly custom sizes. Just last year, Paiste re-released Giant Beats, the cymbals he made famous from Zeppelin II--IV. 2oo2's are Paiste's most successful line largely because of him. The black label versions of the sizes he played go for double what they are worth on eBay because people are looking for vintage Bonham. He still has the drum sound everyone is after. Hope this helps somewhat.