How do you manage multiple releases in multiple environments in continuous integration/delivery?

Although there a probably a few ways to do it, I use the build pipeline plugin https://wiki.jenkins-ci.org/display/JENKINS/Build+Pipeline+Plugin Along with the copy artifacts plugin https://wiki.jenkins-ci.org/display/JENKINS/Copy+Artifact+Plugin

With these, you can create individual jobs for each piece of your environment, and link them altogether.So as in your example, the pipeline would look like:

Build -> Test and Deploy to UAT (2.0) -> deploy to staging(1.6) -> demo(1.5) -> prod (1.5)

Each piece represents a different build in jenkins. The idea behind continuous integration is you create the binaries once, and you carry it down the pipeline, only changing configuration pieces along the way. In a build job, the artifacts are created and then archived. In any jobs after, the artifact is picked up from the upstream job, some stuff is done, and then it get's re-archived for the next downstream job. So the deploy to staging would go to the Test and Deploy to Uat job to get its binary. The entire concept of Continuous Delivery boils down to the the build pipeline. http://en.wikipedia.org/wiki/Continuous_delivery (and yes I did just cite wikipedia).

As for tagging individual binaries for specific environments, that is by definition, not continuous integration. A binary is suppose to be created in a way that it can easily be propagated from one environment to the next. So unfortunately, individual builds for specific environments can never be continuous delivery. You can use jenkins as a CI server all you want, but if your process does not match, you will never achieve true continuous integration.

Braching, merging and checkins always seems to be a touchy subject when it comes to Continuous Integration, so I won't go into it much. But a lot of people share the idea that : "If different members of the team are working on separate branches, then by definition, they not participating in continuous integration process." http://eugenedvorkin.com/continuous-integration-strategies-for-branching-and-merging/

EDIT
For Flagging specific builds, it sounds like your looking to take use of this feature : https://wiki.jenkins-ci.org/display/JENKINS/Fingerprint ... Which gets the job done effectively, giving you the entire life of any individual artifact. A bit more complex solution would be artifactory, which is essentially artifact source control.

I explained the concept of the deployment process above, and without information on your specific environment it is hard to go much further. But for me, for java applications deployed to tomcat containers, the deploy plugin works great https://wiki.jenkins-ci.org/display/JENKINS/Deploy+Plugin

You shouldn't have to worry about selection of which artifact to deploy. The pipeline should be setup to always deploy the latest artifact that was archived in its corresponding upstream job.

Maybe Docker can help you out with this issue. It is able to deploy images of projects to a specific environment. If that environment has a docker client or a docker deamon you are able to request specific information about that environment and the project (to be) deployed on it.

Jenkins can still play a huge part in your pipeline for the integration part and you could let docker do the delivery part.

Docker: https://www.docker.com

Docker plugin for jenkins: https://wiki.jenkins-ci.org/display/JENKINS/Docker+build+step+plugin

Docker also has support for windows machines and .NET.