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Which operating system?
For windows machines, if you're writing a server to scale well, and therefore using I/O Completion Ports and async I/O, then the main limitation is the amount of non-paged pool that you're using for each active connection. This translates directly into a limit based on the amount of memory that your machine has installed (non-paged pool is a finite, fixed size amount that is based on the total memory installed).
For connections that don't see much traffic you can reduce make them more efficient by posting 'zero byte reads' which don't use non-paged pool and don't affect the locked pages limit (another potentially limited resource that may prevent you having lots of socket connections open).
Apart from that, well, you will need to profile but I've managed to get more than 70,000 concurrent connections on a modestly specified (760MB memory) server; see here http://www.lenholgate.com/blog/2005/11/windows-tcpip-server-performance.html for more details.
Obviously if you're using a less efficient architecture such as 'thread per connection' or 'select' then you should expect to achieve less impressive figures; but, IMHO, there's simply no reason to select such architectures for windows socket servers.
Edit: see here http://blogs.technet.com/markrussinovich/archive/2009/03/26/3211216.aspx; the way that the amount of non-paged pool is calculated has changed in Vista and Server 2008 and there's now much more available.