+0
When people say:

I been to a lot of different places in the world.

I been pretty good lately.

Is it still considered present perfect tense? Why is the have omitted and is it proper grammar?
+1
Both sentences are wrong. The word "have" (or its contraction in "I've") is required.
Comments  
Personally I never saw this on paper as well as hearing someone pronouncing it. Maybe you just didn't hear the 've. In this case I've is pronounced "aiv".

It's not a proper word use and isn't considered present perfect. Maybe it's a sort of a particular accent. But it's false.