As a network professional, few things beats telnet to port 80 and openssl s_client to port 443. Or a non-switching hub and packet sniffing.
Nothing beats seeing what is [i[really[/i[ sent. And quite often, errors are due to developers not understanding the underlying technologies and what happens behind the scenes,
One of the reoccurring problems I see are developers who think that when they send a cookie to a client, they are guaranteed to get that cookie back, and that it can be trusted to always follow the expected format.
Another common one is a mistaken belief that a client can't have more than one IP address per session.
So my vote goes to telnet as a very versatile browser.