Generally speaking, the typical home Broadband Router does not by default place any restrictions on outgoing traffic. Some can be configured to manage outgoing traffic, some have limited outgoing options, come have pretty comprehensive ability to manage outbound.
Any "enterprise" class or business firewall will absolutely have the capability to manage outgoing traffic, including free ones (search the site, there are a number of posts on firewalls).
Most sysadmins agree that it is necessary to manage outgoing traffic in order to be a good internet citizen and also to manage bandwidth and performance. For instance, generally outgoing SMTP and POP traffic is only allowed from the mail server, to prevent any malware infected PCs from producing spam. Or, if there is a proxy server to manage browsing, outgoing web browsing traffic is only allowed from the proxy server.