Yes and no. The oil that seems to fill up old fields a bit may actually just be seepage from adjacent areas. One thing for sure, there are lots of old wells that haven't filled up in any really significant way. If it does just come from the earth, the relevant question is how quickly, and most evidence points to it not being all that snappy.
We will never run out of gold, but we will never have as much as we want either. Unless of course we learn to make it at a reasonable price.
And even if we do run out of oil and gas, we can make oil as long as there is oil shale, and that is as common as basalt. Potable water already is another problem though.