Headlamp
Walking pole(s)/
Sleeping Bag,
Gaiters: To keep mud, rocks, and snow out of your boots.
Water purification: This is essential as water for drinking is taken directly from mountain streams.
Hiking Boots: This is the most important item on the list. You'll need a comfortable/waterproof pair of hiking boots which offer plenty of support. Make sure they are broken in before you get to Kilimanjaro!
Other Check list (limit yourself)

1 set of thermal underwear (top & bottom)
1 sleeping bag (rating 0 C or four seasons)
1 warm jersey/sweater (wool)
1 sleeping pad/mat
1 pair of track suit top & bottom
1 light towel
1 polar fleece/down vest
1 pair of light loose fitting cotton trousers
1 waterproof jacket (with a hood) & pants
1 to 2 long sleeves shirts (cotton/wool)
4 pairs of thermal hiking socks
2 to 3 T-shirts/shirts
2 pairs of thermal socks liner
2 to 3 pairs of shorts (with pockets)
1 pair of hiking boots
1 wide brimmed hat / baseball cap
1 pair of sneakers/trainers/takkies
1 pair of warm heavy weight gloves/mittens
1 pair of gaiters
1 pair of light weight gloves (inner gloves)
1 bandana
1 pair of sunglasses/mountaineering glasses
1 balaclava
1 wool hat
1 warm scarf