Here is what I have gathered so far as being important things that help me survive in the cruel world of Valheim. I'm currently still in the swamps, so you might adjust things once you get to the mountains. I still think these rules are a good baseline, that should serve you well no matter where you go.

Additional suggestions and corrections are welcome!

1. Overconfidence is your greatest enemy
That's right. Just rushing in unprepared, because you got that nice, shiny armor without any regards for tactics is a sure death recipe. Or going out in the afternoon thinking: "Ah, just gonna get some stuff, I'll be back before dusk".

Just don't.

2. A well-fed Viking is a surviving Viking
Always being well-fed with the best buff-food your biome has to offer is the singular best survival action you can take. In fact, I dare say that having the choice between the best buff-food on order or that nice, shiny armor... I choose the buff-food. (Of course you should take both.)

That's also why doing corpse runs naked and with an empty(!) inventory is a thing (and actually preferable, because it allows you to run in, snag your stuff, and run away as fast as you can). You can still take a few hits without dying.

3. Better to run and live to fight another day (and carry home that precious loot) than to fight and die alone (and lose said loot)
Pretty much says it all. If you got jumped and start feeling the heat, activate Eykthir and make a run for it. There's no shame in running from an enemy that will get the better of you.

You can always come back tomorrow better prepared and kill their sorry a**es.

4. Pick your fights... carefully (corollary of rule three)
Whenever you engage, be mindful of your surroundings. Try to single out your enemies and pick the weaker ones first. Then, when you laid waste to them, you can stand up against the big guys. Always be on the move. Don't stand still, but be mindful not to go where there could be more (and more deadly) enemies lurking.

5. Be afraid of the dark. Very afraid
Unless you absolutely know what you're doing and what you're up against, it is advisable to stay put at night. Sleep it away in your cozy bed and dream of a nice, bright sunny day tomorrow. This is especially advisable if you're just getting aquainted to a new biome.

6. A hit blocked or missed is a life preserved
I know, some people don't use shields (and bows). But I think they are absolutely essential to surviving in the harsh environment of Valheim. An upgraded shield can block most enemies and make it much easier for you to survive waves of them. A bow is essential to taking out spawners and higher level enemies from afar.

Two star draugr archers? Don't go mano a mano. They will waste you, because you cannot evade their arrows. From afar? No problem. Just plink away at them and actively evade their arrows. Now you can, because you see them coming.

...

That's it for now. If you have more rules or like to post your view of all things Valheim survival, please go ahead!