I am not so sure about extremophiles. They are heavily adapted to their particular niche, but usually underperform in most others.

 

Hmmm... The water bear is polyetremophilic.

 

So you would consider adaptability the most important aspect of an organism's survival?

 

That makes sense, look at where it got us humans...

 

The question is a rather broad one though.

 

What current species lineage is most likely to succeed us here on Earth?[/b]

 

There could be several organisms that succeed us. What about the species that succeed them though?

 

Would that organism be a more advanced one compared to us?

 

Alot of it is time and chance, I think.

 

Mutations...which either make the species stronger, or kill it.

No, actually... We're not. Only if you limit your population to something like primates can you make such a declaration and have anything resembling accuracy. Since you went on to include all life on earth in the rest of your post, I must protest your opening salvo.

 

Humans are NOT top dog.

 

 

With that said... Hands down, bacteria. Currently top dog, and forever will be... depending, of course, on how you choose to define "top dog."

 

Indeed - I concur!

 

Also, an interesting fact - in biomass terms there is more cow on the planet than human.

 

I think there may also be more wheat than either!

 

Also also, the 'evolutionary' value of intelligence has yet to be determined! It could be a bad idea for the long term.