Every year people drown because they step out on thin ice and fall through. So when is the ice thick enough to support walking - and fishing?
You need a minimum of 5 inches of ice under your feet to even consider going for a walk on the lake.
There is no universally safe ice thickness. Each body of water has certain properties that affect how much ice is considered safe. Use common sense, and ask people who have more experience than yourself how much ice is required for safe conditions.
Wear a personal flotation device, better yet a one piece insulated floating suit
Don't fish alone, and let someone know where you will be and when you will be back.
Test the ice in front of you with an ice spud or an auger
Be very wary of river ice, because current makes ice thickness vary quite a bit
Snow is a great insulator, and as such it can make the ice strong, but it can also prevent it from freezing. When fishing on snow covered ice, pay close attention, the snow can hide weak spots and cracks that you would otherwise see.
Slush indicates decaying ice
Always carry a nylon rope and a few large nails, they can provide the grip you need in case you fall through the ice and can't grab on to the edge. Face the direction you came from, kick out with your legs, or use your nails to grab on, and roll off as far as you feel is necessary to be safe again, do NOT stand up immediately, you will likely just fall through again. (self-rescue technique)
If you see someone fall through, do not run toward them, rather extend a rope or an object that they can hold onto.
Again, there is no universal set of rules for how thick ice has to be for safe fishing, but as a rule of thumb, these are "minimum requirements" you should memorize:
2 inches of ice is extremely dangerous, do not even attempt to walk on ice this thin
4 inches of ice may be sufficient to walk and go ice fishing
5 inches may be enough to support snowmobiles ( do not park them close to one another)
8 to 12 inches may be enough to support cars or small pickups ( do not park them close to one another)
15 inches may be enough to support medium trucks ( do not park them close to one another)