1. Respect other people while they are training. This is a broad rule, as it everyone has their own goals and reasons for training, yet this should cover most issues.
2. Learn how to spot someone. If someone asks for a spot, then help them out. You should know how many reps they are doing, how hard the set will be and when if ever they need your assistance.
3. Keep your space clean. This includes wiping down equipment, and also not carrying your entire suitcase to each piece of equipment.
4. Personal hygiene. Enough said, just respect yourself and others.
5. Allow others to focus. When someone is preparing for a big lift allow them space, and do not walk directly in front of them.
6. Share. Try not to take up more equipment or space than is neccesary.
7. Have fun! Realistically if all one wants to do is be healthy a gym is probably not necessary. We all do this for different reasons. Some want to set world records, some want to look better, and for others this may just be a mental break. So work to make your training (and those around you) a fun experience.

I hope as you can see from this short list that respecting yourself and respecting others.