I am sorry to say that I have to retract my "favorite things" status of the Old Navy tank top. They were such a great value, for a long time; but I find that the cotton quality has gone down severely. I guess this isn't too surprising considering that they cost only $6 (on sale) each. I have tons of them, and I guess they'll have to be worn to the gym only.
The good news is that I've found a replacement that's only slightly more expensive. The Gap "favorite ribbed tank" is $14.50 or $10.00 on sale. It's got a finer rib and the cotton feels softer. Overall, it's thinner so better for layering and a bit longer which is good for wearing with low waisted pants. I think they run a bit big though, so size down. 
Another good option is the J Crew "solid washed favorite tank" for $16.50. I think it's a little thinner than the Gap one so the white would be somewhat see-through. Maybe it's a bit too long, but since it's thin material it scrunches up without being too bulky.
For the non-budget constrained, James Perse! He now does his long tank top in a cotton/modal blend $45 at Bloomingdale's, Saks, etc. etc. I love modal, it's softer than cotton and more drapey.
I think the Gap option is the best value and the one I'm going to stock up on. I buy a bunch of these every season, so cheap is good. I can't stand white tanks that don't look pefectly white anymore, so I end up getting rid of a lot of them. And no, I don't like to use bleach because it's too harmful to the cotton fibers.
oh the James Perse one looks great, i love the thick straps and the slim cut of it