The PuTTY executable can be carried around on a USB thumbdrive or shared using Dropbox. However, the PuTTY sessions (profiles) that you created on a computer are stored in that computer's registry and are hence not portable.
An easier way to make PuTTY portable is to install and use PortablePuTTY. It stores the sessions locally in a reg file and so you can use those profiles from any location transparently.
Tried with: PortablePuTTY 0.62