Among the issues some people have had with OS X 10.9 Mavericks, one of the biggest gotchas was a loss of access to SMB network shares -- the connection many NAS devices (Network attached storage), Windows PCs or Linux servers use to provide file sharing.
In my case, I got the double foul. My NAS tried to mount forever and failed; same with a Windows 8 PC on my network. The cause appears to be changes made in the networking stack made by Apple. Apple's SMB2 implementation doesn't work with a lot of SMB2 devices -- even networked drives from Windows machines. [SMB2 is actually used by Mavericks for Mac-to-Mac connectivity, unlike older versions of OS X where AFP was the default. –Ed.]
One easy fix involves changing a little bit of text in your server connection URL. Here's how it works: In the Finder, choose the "Go" menu and select "Connect to Server..." (command-K). Type "cifs://yourservername" and hit Return; the server should mount.
CIFS (Common Internet File System) is just another name for the SMB protocol, but using it in the server URL forces the Finder to use the older (not broken) SMB1 implementation, rather than the buggy SMB2. It worked for me with both my NAS and my Windows PC, so there's a good chance it will work for you.
Apple's Support Boards are filled with users pulling their hair out over this one, so we hope the tip is of use to you.
Thanks to Cammodude for the solution here; he also posts a Terminal tip (at your own risk) for permanently forcing Finder to use SMB1 instead of SMB2.