If you want to use your NAS with a networked media player such as the Netgear EVA8000, D-Link DSM-510 or many others, look for products that include a UPnP AV compliant media server. Note that having a UPnP or any other media server isn't necessary if you're using a computer as your media player, or if you copy files to your computer or other device to play them. But networked media players rely on media servers such as UPnP AV to both find and play media.
Some NASes are starting to include iTunes servers that will allow machines running iTunes to find and play iTunes content. You'll also find some products advertising DLNA or Viiv certification or compliance, neither of which matter as much as UPnP AV.
NOTE: Any current NAS is fast enough to handle photo and music serving. Most can also handle one or two video streams.
You'll probably want some ability to control access to certain NAS folders, which is where Access Controls come in. Almost all NASes provide the ability to create user accounts and set user-level access permissions. It's also increasingly common to also find group-level permissions supported, although they are not as much a given as user-level.
If you plan to use your NAS in a large-network environment, you may be interested in having the NAS get its user and group permission information from NT or Active Directory (AD) servers. This is not universally supported and some manufacturers, such as Buffalo, have split their product lines into models with and without AD / NT support.
As mentioned earlier, all NASes support SMB/CIFS, which means that virtually any modern operating system will be able to access its shares. But if you're running a Mac OS shop, you might prefer using AFP (Apple Filing Protocol) or even NFS (Network File System) instead. You'll have more luck finding products that support AFP than NFS. And sometimes when NFS is supported, the implementation is essentially unusable, as it is on the Hammer myshare, because the full path to the share is undocumented.
In an effort to pull you in their direction, manufacturers often pack other features into their NASes, mostly in the form of additional services. This is relatively easy to do, since most NASes are based on Linux and there are plenty of handy open source modules that can be added relatively easily.
The most common "other" service you'll find is FTP, which provides another way to get files into and out of the NAS. Implementation, however, is a mixed bag, with some products providing only anonymous FTP.
Print servers for USB printers are next most common, but primarily support printing from Windows machines. You might have luck getting printing from Mac OS X clients to work, if you have a Postscript printer and suitable PPD file.
Most of the print server implementations are "black boxes" with only the ability to enable or disable the feature. Some give you the ability to kill the entire print queue, but none that I've seen allow you to monitor the print queue or kill individual jobs. My advice is not to buy any NAS based on its print serving feature. Think of it more like an unexpected gift if it works!
Web (HTTP) servers are another common feature, with various implementations. For example, Infrant's ReadyNASes allow stored files to be accessed via a web browser. This can be a handy way to make files available remotely or to devices that don't support SMB/CIFS browsing. Some NASes even support HTTPS, which is probably more important for secure, remote administration than local file access.
Synology, on the other hand, has taken a more aggressive approach, including both a PHP interpreter and MySQL database in their HTTP servers. This allows you to use their NASes as full-blown web servers supporting dynamic web applications.
One last feature worth mentioning is download clients. This is the ability to queue up a list of Torrents, FTP and/or HTTP files and then have the NAS automatically download them to a selected share, without requiring an external computer. Synology and Thecus lead the way in introducing this feature, which is now seems to be moving into the mainstream.