The following list of points outline what I think resembles good social grace in the gym. The points focus on creating a safe environment, but also on creating a supportive one, too.
Creating a Safe Environment
1. Avoid walking in front of someone who is using the mirror to check their form during an exercise. If the exercise is new to them, or weight especially challenging, they might need to use the mirror. By blocking their view, it can lead to a serious injury.
2. Remove the weight plates from the squat rack, or Olympic bar, after you're done with your exercise. The next person to use the equipment might not be as strong as you, and might injury themselves trying to remove them. If you see someone struggling with removing weight plates, please help them if you can.
3. Don't talk to someone in the middle of an exercise, whatever the weight they are lifting. The weight might seem very light to you, but to them it could be very challenging. Distracting them can easily lead to a very nasty accident.
4. If you see someone struggling with an exercise offer to spot for them. This could avoid any potential accident occurring.
5. Give people enough physical space to safely carry out their exercises. If someone feels you are invading their space whilst they are carrying out an exercise it can be very distracting for them, especially if you are not giving them the room they need to safely perform the exercise. This can also easily lead to a very nasty accident.
6. Clean up big pools of sweat from the floor or stretch mats, people can easily slip on them.
Creating a Supportive Environment
7. Work in your sets with other people so you can all share the same equipment.
8. Limit your time with popular pieces of equipment at busy times.
9. Check that nobody is using the equipment you need before you start your exercise. Also, when you have finished with the equipment let people know who have been waiting to use it.
10. Wear clean training kit. The guy who wears the same kit all week can disrupt everyone's training session!
11. Avoid taking up too much physical space in the gym during busy times, be aware of other people.
12. Always aim to be friendly towards other gym-goers and support them in whatever way you can.