I wondered why sometimes the Home and End keys work as expected during a SSH session via PuTTY and some other times it just writes tildes (~) instead. When writing long commands it is a real annoyance having to press down the left arrow to get back to the beginning of the command.
A simple solution which worked for me was to change the Terminal-type String under the Connection > Data tab from the default “xterm” to simply “linux”:
Now you should be able to use your Home and End keys to easily move the cursor back and forth during a SSH session using PuTTY.