Off the top of my head, I can name four national drugstore chains: Walgreens, CVS, Duane Reade, and RiteAid. On top of that, there's Soap.com and Alice, two online drugstores. And some very quick research (wikipedia) shows me that Walmart, Kroger, and Target, among others, are also major players in this area of business. Also, apparently, there's Drugstore.com, though this (and apparently DR as well now) is owned by Walgreens.
Essentially, the pharmacy market seems to an outsider (me) to be an extremely over-saturated market. We live a block away from a Walgreens, and only two blocks away from that is a CVS. This is ridiculous. There seems to be no reason why the drugstore market needs to be this large.
And then there's all the pharmacies that no longer exist but were once big chains. Eckerd. Phar-Mor. So even if we agree that the market is over-saturated now, imagine how much worse it used to be!
One could suggest that there's serious room for disruption in this market, that whomever enters and provides a vastly better service should be able to seriously winnow the market down, removing some of the lesser competitors (read: RiteAid). This is probably the goal behind the online drugstore competitors, but these stores fail to address the pharmacy aspect of drugstores. In other words, they provide the soap and toilet paper and toothpaste, but can't easily fill prescriptions in a way that works for customers.
I'm not actually convinced that a serious competitor could come in, however, to disrupt this market. I think that the barriers of entry are too high. Not the traditional barriers of entry, such as overhead or cost, or other issues caused by a market controlled by too few entities (such as a monopoly or oligopoly), but a different kind of barriers to entry, caused by the opposite. I think the drugstore market is so over-competitive, there's no room for another competitor, no matter what edge they have.
The market needs to first shrink itself, through more acquisitions or other ways of eliminating some of the participants, before a true disruptor can come in and change the drugstore world for the better. I don't know how accurate this is, but it seems reasonable: there are so many competitors, customers wouldn't even notice a new one.
Or it could be that we truly do need that much shampoo and bug spray. So large is our appetite for these things that the drugstore market is not in fact over-saturated, but properly large. I don't buy this argument though. There's just too many of them.