I'll start, for the Celebrity Infinity. This description and the photos should be identical or similar for all of Celebrity's Millennium-class ships: Millennium, Constellation, Infinity and Summit.
The Infinity has a large, well-lit gym at the top, front of the ship with a wall of windows facing forward. Half of the gym is a wood-floored aerobics area, the other half is filled with weight and cardio equipment. There is a relatively small free-weight area with dumbells and various benches. As shown in the attached photos, the equipment consists of the following:
Five benches: two flat, two incline adjustable, and one decline adjustable.
Dumbells from 5 to 50 lbs, plus 1-10 lbs handweights.
Multiple Swiss balls, mats, and steps.
16 Spinning bikes.
14 Treadmills, facing the forward windows.
2 rowing machines.
4 recumbent bikes.
4 "regular" bikes.
4 eliptical trainers
16-piece Nautilus weight set. (The ergonomics aren't great, but it's very complete).
The gym is part of the spa, which has large mens and women's locker rooms; each with day lockers and showers, along with towels, razors, puffs, etc. There is a large dry sauna in each of the locker rooms, with a dramatic round window facing the sea. There is a coed steam room area (the "Persian Gardens) with an extra charge of $30/day or $99 for a 7 day cruise. There is also a large Thallassotherapy pool attached to the spa, with various high-pressure water jets to massage sore muscles, and two bubble beds.
How about describing some other ships?