After reading through this whole thread there are some things I would like to add that can be of vital importance and have not been discussed.
Number one: Your ENVIRONMENT
This is not just conditions, this is the ecology that surrounds you. I truly think this is of vital importance. If you do not understand your environment, how can you be a safe diver, to yourself, your buddy and to the wonderful places we dive. I can not tell you how many time I have been on a vacation diver herd boat and encountered divers who have no idea that coral is an animal, that it is alive, that it is easily damaged or killed. People who have no idea the ID or differences between corals, sponges, algae and inverts. People who do know know the dangers certain organisms can pose. Who have no idea of what certain animal behaviours mean. There is a huge difference between the behaviour of an animal and responses to your behaviour. For instance, a Moray, resting and breathing some people think is aggressive, and the actual aggressive behaviour, or hunting behaviour. When you understand these things you can better gauge you safe distance, and even anticipate their actions and be able to see some very interesting things others will miss. One recent dive I was on there was an eel free swimming during the day, it seemed like it was in a hurry, everyone else swam off and I hung back for a few seconds watching it. I got to see it in an epic battle with a lobster and everyone else missed it. Understanding your environment is also of vital importance when traveling to new places. If you are going to places with a high density of poisonous animals, you really need to know.
As far as asking for buddy checks, some people feel uncomfortable, think if its as uncomfortable as an emergency situation would be. Know the difference between a DM who is looking out for you and others, and one who could care less. Some people like to get their DM so they can brag about it or try to impress the ladies, not because they have a true love of what they are doing. I know so many new divers who go from one cert right into the next without gathering experience dives first. How do you reinforce your learning without practice? Another issue is courtesy. I dive with a dive hood. My hoods have ears/nudibranch on them (yes, I'm a nerd like that). On my last trip on a night dive, I had one couple shinning both their lights on me for the entire safety stop. I was SWARMED with worms and little biteys. Seriously. Think about what you are doing in regards to others. If you are interacting with others in a way that compromises them, startles them or changes their behaviour or reactions, you are not being a safe diver.
Knowing and understanding the limits of others is huge. I know a lot of new divers who are so stoked about diving and proclaim, EVERYONE SHOULD DIVE! No, not everyone should dive. To be a safe diver you have to have the ability to stay on point, to notice things around you and to multitask. You also have to be able to deal not only with your own person/equipment, but your buddy's as well. This speaks a lot to fitness. If you opt to dive with someone who is not there, know that even though they might be able to save their own arse, they might not be fit enough to deal with both themselves and you, which would leave you vulnerable. Take EFR and Rescue Diver, you will learn so much as well as realize exactly where your abilities are at. I see so many couples where you can immediately tell the partner (often smaller females) has been "convinced" to dive. What would she do with her buddy/partner unconscious on the bottom? My spouse is one of those people who should never dive. He is a genius in his field, but can not multitask or notice even major things in his environment and he is not good in emergency situations, he panics. As much as I would love to share this with him, I know it would put both of us at risk.
Lastly, buoyancy, buoyancy, buoyancy. I take more weight than most, I have had people doubt me all the time. Reason, I used to be very overweight and lost it extremely rapidly. I have a lot of excess skin, which is not obvious, but it is very buoyant. If I dive with what is recommended to me by most, I can not do a controlled ascent at the end of my dive. Check your buoyancy, frequently, with different equipment, conditions, and changes to your physiology. Two women weighing 130 can have very different needs, one might be more "fluffy" and the other does P90X everyday...
Last thing, as echoed by many, arrogance and ignorance is a terrible thing. Never think you know everything and never stop learning. And please, learn everything you can about your environment and animal physiology and behaviour. It might not save your life, it might save theirs.
Carey