The last surviving creatures on Earth will be microbes
When the sun is much hotter and the oceans boil out...Studying other stars has taught us a lot about what will eventually happen to our sun, hundreds of millions of years in the future (not exactly an immediate concern, but interesting to know). It is predicted that in about a billion years, the sun will generate more light and thus more heat; enough to boil the Earth's oceans and make them evaporate! One might expect that any life remaining on the planet at that point would disappear, but that would be underestimating microbes (esp. of the extremophile kind -- some of these can live in what seems to us like impossibly harsh conditions).
At least, that's what a computer model to predict what will happen to the Earth when the sun heats it up shows. In a world with very little oxygen, an atmosphere hotter than 100 celsius, high-salinity oceans, etc, nothing else could survive and these microbes will be the last surviving creates on the planet.
But even these hardy microbes wouldn't last forever on the inhospitable future Earth:
a group of microbes called extremophiles would be the only life forms left.
These tiny organisms are found on Earth today, and can cope with hostile environments.
These, the scientists said, would be the only creatures that could withstand the heat, aridity and poisonous atmosphere of this future Earth. They believe that they would probably be clustered around the last drops of water deep underground.
Eventually as conditions worsen they too will vanish, and in about 2.8 billion years, Earth will be devoid of all life.(source)
If that sounds bleak, just remember that we're talking about a billion+ years in the future. We won't deal with any of that, but humanity needs to figure out rapidly how to live sustainably on Earth right now.