Check this site out... if you haven't already, that is.
What they say sound like well reasoned arguments, but I don't agree with them (that may be due to the way I (we?) have been brought up, I don't know).
What do you guys think?
Yes I agree with you Blowtorch, one excerpt from there:
As per the above, suppose all humans on this planet stop breeding, what will happen after 50 years 
Regards,
Tayyab
You gotta love this quote:
That would seem to be an extremely safe statement. I guess the last few humans could travel to the moon or something. Other than that seeing "no human beings on the planet" is gonna be rough.
Actually, the life of our sun is finite. So, in theory, Earth will be vaporized when the sun runs out of hydrogen for fuel and turns into a nasty red giant. Estimates for this are in the 5 billion year range. Somehow, I don't think people will be here to worry about it.
Actually it will be well before that the Earth is uninhabitable. The Sun is gradually releasing more energy as the core piles up more helium and the hydrogen burning zone expands. If I recall correctly a few billion years ago when life first started it was 30-40% less luminous. Within another billion or two it is expected to make it so hot that Earth's oceans boil away and the surface becomes too hot for any life as we know it (other than some bacteria I suppose).
Sorry, the former astronomy geek in me took over for a second there. 