By "stickiness", I assume that you are referring to something like PHP's "_SESSION" variable.
App Engine prefers developers to use a REST (Representational State Transfer) architectural style where the server is assumed to be stateless:
"Stateless: each request from client to server must contain all the information necessary to understand the request, and cannot take advantage of any stored context on the server"
However, maintaining server state is possible. Here is a link to a web framework running on App Engine that enables server-side continuations: