Required Ports for Steam
The following are ports you need to have open on your router or firewall for Steam to operate normally.
 

1. To log into Steam and download content:
   1. HTTP (TCP remote port 80) and HTTPS (443)
   2. UDP remote port 27015-27050
   3. TCP remote port 27015-27050
2. Steam Client:
   1. UDP remote port 27000-27100: Game traffic
   2. UDP local port 27031-27036: Remote Play
   3. TCP local port 27036: Remote Play
   4. UDP remote port 4380
3. Dedicated or Listen Servers:
   1. TCP local port 27015 (default): SRCDS Rcon port
   2. UDP local port 27015 (default): gameplay traffic
       
4. Steamworks P2P Networking and Steam Voice Chat:
   1. UDP remote port 3478
   2. UDP remote port 4379
   3. UDP remote port 4380
   4. UDP remote ports: 27014-27030
       
      Note: Many schools, universities, business networks and proxies block required ports for Steam operation - please consult your network administrator to ensure the required ports are open if you are using a university/business network or a proxy. 
      Ports required for Steam can not be re-mapped to HTTP or reconfigured to a custom port range.
       
5. For generic Steam HTTP/HTTPS requests, your proxy should allow the following domains:
   • steampowered.com
   • steamcommunity.com
   • steamgames.com
   • steamusercontent.com
   • steamcontent.com
   • steamstatic.com
   • akamaihd.net

Most of the non-web traffic is usually UDP but can be TCP as well. For that, the IPs will all be from the Valve network (AS32590), and a list of those IP blocks can be found here