CloudBees provides an enterprise Continuous Delivery Platform that accelerates the software development, integration and deployment processes. Building on the power of Jenkins CI, CloudBees enables you to adopt continuous delivery incrementally or organization-wide, supporting on-premise, cloud and hybrid environments.
Just a quick update: sticky sessions (also known as session affinity) are now available for apps on CloudBees. This means that the CloudBees load balancing can "stick" users to backends if that is what your application (or your preferred framework) requires.
You can read more about how to turn sticky sessions on here - there isn't much to it - turn it on, or not!
It is worth remembering that along with load balancing, there are goodies like auto-scale, app clustering (and session store), and zero downtime deployments to read about and enjoy (don't worry, you don't have to do much). Databases are always master/slave pairs, backed up for you - all of this helps a little bit for HA and scalability, when you need it.
Note also there is this handy excuse generator (not affiliated with CloudBees), should you need it.