Don't underestimate how cold it is at night and particularly on summit night; bring as many layers as possible (including inner gloves and socks; I had 8 layers under my jacket for the summit and was toasty warm...bar the exposed bits like my nose!), and invest in a really decent down sleeping bag and jacket, as well as a good water/windproof jacket and trousers. Lots of antiseptic Wet Wipes are a must, plenty of tissues, energy snacks (nuts, chocolate, etc - I ate SO much on summit night), thermal trousers, Nytol, ear plugs, silk sleeping bag liner (warmer & lighter than cotton), walking poles (never used them before but was very grateful for them for the summit), head torch, Vaseline for your nose is a good idea as it will be red raw after summit day; and not forgetting a whole separate wardrobe for the beach...EVERYTHING from the mountain will be filthy! Plus bring plenty of individual bags to separate things in your kit bag, otherwise you're constantly rummaging around for the little items. Lastly, big waterproof sacks for separating your clothes, and keeping the dirty things away from anything clean.
Everyone says drink plenty of water; I brought a 2l camelbak and 2 x 1l bottles and really needed all of them, on some days I was drinking up to 7l of water. On the whole I didn't suffer from the altitude, so I can only assume that helped. Also make sure you eat plenty, as you're burning a lot more calories than normal - I ate like a horse for the entire 2 weeks (and drank plenty on Zanzibar!) and I still lost half a stone in weight!
I'd suggest hiring the mattresses - they're fairly comfy as camping mattresses go, much more so than my thermarest - and much warmer!
Oh, and bring a spare battery for your camera - there's no charging facilities on the mountain and you don't want to run out of battery before you get to the summit!
Lastly, enjoy it! The scenery is stunning on the mountain, so look up and enjoy every day of it - it's not all about making it to the top, it's as much about the walk. I loved every second of it, and if I hadn't got to the top I wouldn't have enjoyed it any less.
One word of warning though - check and double check that your connecting flights from Kilimanjaro to Zanzibar have been confirmed by the African Walking Company.... Ours weren't and 3 of our group got bumped off the flight.