Freestyle project

Tags are supported using the default configuration. This assumes Branch to Build filter is set to an empty value. If you don't want tags to be processed, they can be disabled from either the Bitbucket or Jenkins side.

Pipelines

Pipeline jobs support tags. It requires setting Branches to Build parameter to **/**.

Multibranch pipeline with Git plugin

As of September, 2018 it's not supported. Git plugin represents tag as branch and then it gets filtered out

https://github.com/jenkinsci/git-plugin/blob/master/src/main/java/jenkins/plugins/git/GitSCMSource.java#L628

Multibranch pipeline with Bitbucket Branch Source plugin

As of September, 2018 it's not supported. Similar issue as above

https://github.com/jenkinsci/bitbucket-branch-source-plugin/blob/master/src/main/java/com/cloudbees/jenkins/plugins/bitbucket/hooks/PushHookProcessor.java#L163

More details here:

https://issues.jenkins-ci.org/browse/JENKINS-51063