Routers are being marketed to provide one or more of these functions. This is especially needed in the SOHO environment for security. SonicWALL SOHO routers, WatchGuard SOHO routers, and WebRAMP all make this class of router. Of course, Cisco, and Lucent do them for business. They provide NAT and Proxy services normally and usually add DHCP for addressing in the internal network.
Firewalls can also be software applications.
NT Proxy Server is a business application. ZoneAlarm is a software application as is Black Ice Defender. All direct connections to the Internet need some mix of these functions to protect against outside intrusion. I employ all of these functions in my network. I use a MultiTech ProxyServer in my network mix as well as software firewall versions such as ZoneAlarm.