NB: This is for v 1.6.93 (which I can't select in the Version dropdown but is the only version currently available from Mojang)
The 'forgot password' link in the Launcher does not work. It goes to:
http://help.mojang.com/customer/portal/articles/329524-change-or-forgot-password?ref=launcher
..which just resolves to the generic https://help.minecraft.net/hc/en-us address.
The v1.6.93 version of the launcher hasn't been updated in years and will cease to work very soon. Please update to the new launcher version (2.1.xxxx) as soon as possible. It's available for all OSes that Minecraft can be played on. → https://www.minecraft.net/en-us/download