On my first character, who is now level 40 and being retired, I had no points in stamina, as restoration allowed me to basically have infinite. But I'm starting a new stealth dual-wield character soon and I'm wondering if I should put points into stamina since I wont be using magic.

It's my highest.

Maybe like 100 magic 200 health 250 stamina.
Then again I'm a thief/ assassin build.

More power attacks/Sprinting/Aiming with bow
Plus you can carry more stuff.

If you're not going to enchant something to boost stamina massively, and you're not going to carry a bunch of Restore Stamina potions... you're going to want to put points into it. It's critical, and you'll be astonished at how quickly you lose it the first time you actually have to stand up and fight someone/something.

It's kind of, like, very important. And stuff.

Considering it determines sprint speed, attack power and duration for melee, etc.

It's quite important, actually. Many combat techniques, such as blocking and power attacks, rely on it.
Also, the higher it is, the faster it regenerates. 5% Max Stamina per second.

Additionally:
Carry Weight capacity = 250 + Stamina/2

Hope that helps.

Its my highest stat too.

Carry capacity is exceedingly useful.

I use +magicka regen enchants to have enough magic in combat, and I rely on good armour to not need much health, and a high enough stamina to not need to worry about other things.

Stamina also incorporates strength so affects how much you can carry and probably how much damage you do with melee weapons but that bits a guess. If you use bow or weapons is important as its what powers tour attacks.

I have 250 stamona and can do 4 power aytacks before exausting all stamins. Power bashing is important and bashing too since u use it to prevent enemies from attacking you and that also takes stamina.
Basically u need stamina to perform powerful and important uses. Its exActly like magicka for magic.

And now to provide the dissenting opinion... My not-quite-40 stealth archer has taken a couple stamina bumps on general principle and I often debate with myself over whether those points were a complete waste or not. I rarely get into melee and, when I do, I tend to just use normal strikes, not shield bashes or power attacks, so the only thing that ever burns any of my stamina is bow zoom - and I don't use that very much either, because the effective range of bows in Skyrim seems to be short enough that, if I can't line up the shot without zooming, there's no way it's going to register as a hit anyhow.

Even since I've started doing melee backstabs (after getting the x15 dagger sneak attack), I haven't felt a need for more stamina because, even if I do use a power attack, it doesn't matter how much of my stamina bar it consumes, because the target's going down in one hit. It doesn't matter if you pass out exhausted on the floor when the other guy is already dead.

The only benefit I've seen to increasing stamina for my character has been the increase in carrying capacity - and a paltry 5 extra encumbrance (a whole 1.67% increase over what you start with!) per stamina pick doesn't strike me as anything to get excited about.

For a thief/assassin i don't really think its needed much so long as you play strictly as stealth, but for warriors it is pretty critical because once you lose the ability to bash because you have no stamina then you are in some serious trouble from the NPCs rocking 2h.

I think i agree. Im not much of a stealth character yet. Will get there later in my character.
If i go head to head i heavily rely on the moves that cause staggering. Its imperative for me.
However, as far as i can tell, the 250 stamina i have seems to be enough for most og my encounters this far. (im lvl18).