I think it shows a lot, considering I think it's still in the ballpark of under 8,000,000 patents issued in the US total. It shows a fair amount of intelligence, original thinking, and follow-through. Patent prosecution can last years from when the application is filed to when it is issued as a patent. It's more rare when the application is filed to it being allowed right away, because very very few things at this point are clearly not obvious compared to the prior art.
I guess bottom-line, it can't hurt you. I disagree that a lot of people have patents issued in the course of their research. If that were the case, there would have been way more patents issued in the US considering the large amount of research that has been undertaken since the patent office has been up and running (since 1790).
Most of the time, the rights for the patent are assigned to a corporation/company whose resources were used in the discovery of the invention, i.e. the company retains any profit generated and the right to exclude other corporations and companies from using the invention for the full term of the patent assuming maintenance fees are paid at 3 1/2, 7 1/2 and 11 1/2 years from issuance. Of course, others are always welcome to license the patent, but that's another story.