This may seem like an obvious one, and alot is probably covered in other sections, but it is still an important one. The ramblers website has a very exstensive safety section here, so we won’t go into explicit detail with everything on here, but touch on some of the more important aspects.
Make sure that you take a map and compass with you, and KNOW HOW TO USE IT! GPS devices, smartphones etc are a very handy tool, but the battery life can be problematic. You also need to make sure that you have enough power in your phone battery in case you need it in an emergency. Also, make sure that you have studied your map and you are aware of the terrain as well as any potential hazzards.
As I mentioned above, electronic devives of all shapes and sizes can be useful, as long as you know their limitations and how to overcome them.
Know your weather forecast. Always use a reputable weather forecaster; I use the Met Office, and I find them to be fairly accurate, and they also have a mountain weather section.
Depending where you are walking, the weather can change very suddenly. I have been walking in brilliant sunshine in shorts and a t-shirt, only to have to put on long trousers and a rain coat the next minute. Always be prepared for the worst that your terrain can throw at you.