I started using Burp Proxy three months ago when an application I was testing required NTLM authentication. Paros, my regular proxy, wasn't up to it and I stumbled on Burp. Here are some reasons why I've come to like Burp Proxy:
Burp supports Basic, Digest and NTLM authentication for proxies and web servers.
We can add as many upstream proxy servers as required with Basic, Digest and NTLM authentication too.
It keeps a history of all sent requests, viewable in the browser. It also keeps track of the ones that were modified and allows the user to resend the requests directly from the history.
Easy to write request/response header replacement rules.
Burp Proxy is from Portswigger; they also have a spider and an automated scanner.