I currently have a small socket server that I'm trying to convert to a web server. Basically it dumps XML to anyone connecting to it. At the moment, it's not a web server as it listens to a non-web port (1337).
I know that both 80 and 8080 are accepted web ports, but none of those are free on the machine I'm going to use. Are there any other web ports available? Or how do I configure a windows machine so that e.g. port 1337 is web?
You just start listening on the port. Viola. It's a server. That simple. Oh, and you have to tell your audience which port to use.
To be more complete: it's a web server not because of the port, but because of the language spoken on that port. You can serve HTTP over any port, which is one of the ways back-door-style malware gets around misconfigured firewalls.
Well for the most simplistic method append :port to your URL such as http://192.168.1.1:1337
I may be misunderstanding your question though.
What you probably need is to implement (in order to implement an easily usable web service, which I assume is what you are aiming for) the http protocol and probably SOAP or REST, not select a port number. Tell us what language you are using, and we might be able to suggest a suitable framework.
What @fictoris said. Or setup your webserver to redirect http://myapp.com to the correct port as well.
There's nothing really magic about the ports you are talking about. And really it's just port 80 that's standard HTTP. 443 is the standard for secure HTTP though (HTTPS).
If you have to run on a non-standard port you must specify that port in every (non-relative) URL: http://localhost:13828 ...
If you need to use port 80 you might be able to redirect the incoming client depending on what demain it requested though.
Here is a list of all the TCP/UDP ports that have official designations and the hi-jacked, oh I mean unofficial ports that are known. Hopefully that will give you an idea of what is going on "out there."
Note the "Dynamic, private or ephemeral ports: 49152–65535" section at the bottom.