I'm still= I am still. It is correct. It is the same as saying I am still.

I still= Is not correct. Most people would understand you but it is incorrect.

"Still" has multiple uses. When you say "I'm still..." it sounds like "until now (and later maybe)". For example:

<em>1. I'm </em><em>still</em><em> sad = I was sad </em><em>before,</em><em> I'm sad </em><em>now</em><em>, and I </em><em>might be</em><em> sad</em><em> later</em><em>.</em>

When you say "I still..." it sounds like "even if". For example:

<em>2. I'm not hungry, but I will</em><em> still</em><em> eat some snacks = </em><em>Even if </em><em>I am not hungry, I will eat snacks.</em>

The emphasis with "still" in number 2 is the contrast. "I am not hungry." and "I will eat snacks" do not make sense to combine, unless you use "still" to emphasize the contrast.

Another example:

<em>3. My dog ate my homework, but I </em><em>still</em><em> love my dog. = </em><em>Even though </em><em>my dog ate my homework, I love my dog.</em>

Hope this was helpful :)