Very popular free SSH client. Connects to hosts via secure shell, telnet or RS232. This program has been around for ages. It may not be the prettiest one, but it does the job and it is free.
Ranked in these QuestionsQuestion Ranking
Pro De facto standard client for SSH, Telnet and Rlogin
PuTTY is one of the oldest and most popular clients. It has earned the trust of a great number of users over a long period by being reliable, offering useful features and helpful support. It got into the 15 Essential Open Source Tools for Windows Admins list by InfoWorld.
Pro Source code available
Full source available. Compile and modify it yourself.
Pro Lightweight and portable
Doesn't require much resources (memory and hard-disk). Can even be run on a system by just downloading without install.
Pro Can be used on any Windows computer, even without admin rights
Con Can not save passwords
Anyway, you can use "PuTTYgen" to generate a key pair, then use "Pageant" to do a password-less SSH remote login.
Con Lacks features
It is JUST an SSH client. There are many other options with built in X-servers, Multitabbing, etc.
Con Ugly design, too simple
Con Tedious logging/tracing
Its tedious to set up logging and tracing (e.g. for serial connections).
Con No global settings
If you want to change a setting for all your connections, you'd have to do it individually.