How can I prevent two Jenkins projects/builds from running concurrently?

The Locks and Latches plugin should resolve your problem. Create a lock and have both jobs use the same lock. That will prevent the jobs from running concurrently.

1. Install the plugin in "Manage Jenkins: Manage Plugins."
2. Define (provide a name for) your lock(s) in "Manage Jenkins: Configure System."
3. For each job you want to participate in the exclusion,
   1. in ": Configure: Build Environment," check "Locks",
   2. and pick your lock name from the drop list.

The Lockable Resources Plugin. Simple and working well for me May 2016.

Install the plugin. In Manage Jenkins > Configure System go to Lockable Resources Manager.
Select Add Lockable Resource. Enter values for field: Name and hit Save. Warning: Do not enter spaces in Name field.

In Jenkins > job_name > Configure > General, Select checkbox: This build requires lockable resources. Enter name or names in value for field: Resources.

Start a build. Under build #number select Locked Resources. You should see something like:This build has locked the following resources: resource_name - resource_description.

Start a different build which uses the same resource. You will see Build Queue in Jenkins status/menu showing job name. Hover text shows Started by, Waiting for resources resources_list, Waiting for time.

(also resource tags/labels can be used)

Adding screenshot of Job Configuration page as there seems to be a problem for some users where "This build requires lockable resources" is not visible: ** when the checkbox is not selected you should only see "[_] This build requires lockable resources"

1 December 2021
Use Build Blocker plugin, Install from Manage Jenkins > Plugin Manager

For example, you have two pipelines React-build and React-tests:
Go to React-build -> Configure -> Block build
if I don't need React-tests to run concurrently with the current React-build job, add it in the blocking list,

Regex expressions can also be used, i.e. to avoid concurrent builds for all projects starting with React-, add React-.* to the list,

Replace React-tests with any pipeline-name you want not to run parallel, with global or node level options,

When tried to run any blocked jobs together with configured React-build job, it gets moved to pending state,

EDIT: Below information is effective as of 04/10/2014

Exclusion plugin, https://wiki.jenkins-ci.org/display/JENKINS/Exclusion-Plugin Very useful if few build use the same resource - e.g. a test database. All you need to do is to update configuration of all jobs using this resource and as a result they will never run in parallel but wait for others to complete.

Taken from : http://www.kaczanowscy.pl/tomek/2012-07/jenkins-plugins-part-iii-towards-continuous-delivery

This plugin does block two or more jobs from running in parallel.
To test, do this for job1

1. Configure
   
2. Under Build Environment check "Add resource to manage exclusion."
   
3. Then Add -> New Resource -> Name -> lock
   
4. Under Build -> Add build step
   
5. Critical Block Start
   
6. Add build step -> Add whatever you want to add.(add sleep 15 to make sure it lasts longer to check concurrency.)
   
7. Add build step -> Critical block end
   
8. Repeat the above steps for job2, make sure you use the same lock name 'lock'.
   
9. manually build both jobs concurrently.
   
10. Monitor the run progress under jenkins -> Exclusion administration.