Have ran into the same issue however I am running Jenkins 1.529. Same situation, some manual builds will work however all polled builds fail every time. I do not have the mailer plugin installed and its not within the plugin directory on disk.

OS: Redhat 6.4
Jenkins: 1.529
Git Plugin: 1.5.0
Git Client Plugin: 1.1.2

Please let me know if you need more information.

Fetching upstream changes from origin
Commencing build of Revision bac119abc399796146043fa057efe3e485a65256 (origin/dev)
Checking out Revision bac119abc399796146043fa057efe3e485a65256 (origin/dev)
FATAL: hudson/tasks/Mailer$UserProperty
java.lang.NoClassDefFoundError: hudson/tasks/Mailer$UserProperty
at hudson.plugins.git.GitChangeLogParser.parseCommit(GitChangeLogParser.java:70)
at hudson.plugins.git.GitChangeLogParser.parse(GitChangeLogParser.java:49)
at hudson.plugins.git.GitChangeLogParser.parse(GitChangeLogParser.java:23)
at hudson.model.AbstractBuild.calcChangeSet(AbstractBuild.java:922)
at hudson.model.AbstractBuild.access$600(AbstractBuild.java:105)
at hudson.model.AbstractBuild$AbstractBuildExecution.defaultCheckout(AbstractBuild.java:681)
at jenkins.scm.SCMCheckoutStrategy.checkout(SCMCheckoutStrategy.java:88)
at hudson.model.AbstractBuild$AbstractBuildExecution.run(AbstractBuild.java:581)
at hudson.model.Run.execute(Run.java:1603)
at hudson.model.FreeStyleBuild.run(FreeStyleBuild.java:46)
at hudson.model.ResourceController.execute(ResourceController.java:88)
at hudson.model.Executor.run(Executor.java:247)
Caused by: java.lang.ClassNotFoundException: hudson.tasks.Mailer$UserProperty
at org.apache.tools.ant.AntClassLoader.findClassInComponents(AntClassLoader.java:1365)
at org.apache.tools.ant.AntClassLoader.findClass(AntClassLoader.java:1315)
at org.apache.tools.ant.AntClassLoader.loadClass(AntClassLoader.java:1068)
at java.lang.ClassLoader.loadClass(ClassLoader.java:266)
... 12 more

FATAL: hudson/tasks/Mailer$UserProperty
java.lang.NoClassDefFoundError: hudson/tasks/Mailer$UserProperty
at hudson.plugins.git.GitChangeLogParser.parseCommit(GitChangeLogParser.java:70)
at hudson.plugins.git.GitChangeLogParser.parse(GitChangeLogParser.java:59)
at hudson.plugins.git.GitChangeLogParser.parse(GitChangeLogParser.java:23)
at hudson.model.AbstractBuild.calcChangeSet(AbstractBuild.java:922)
at hudson.model.AbstractBuild.getChangeSet(AbstractBuild.java:896)
at hudson.model.AbstractBuild.getCulprits(AbstractBuild.java:420)
at hudson.model.AbstractBuild.getCulprits(AbstractBuild.java:417)
at hudson.model.AbstractBuild$AbstractBuildExecution.post(AbstractBuild.java:733)
at hudson.model.Run.execute(Run.java:1628)
at hudson.model.FreeStyleBuild.run(FreeStyleBuild.java:46)
at hudson.model.ResourceController.execute(ResourceController.java:88)
at hudson.model.Executor.run(Executor.java:247)
Caused by: java.lang.ClassNotFoundException: hudson.tasks.Mailer$UserProperty
at org.apache.tools.ant.AntClassLoader.findClassInComponents(AntClassLoader.java:1365)
at org.apache.tools.ant.AntClassLoader.findClass(AntClassLoader.java:1315)
at org.apache.tools.ant.AntClassLoader.loadClass(AntClassLoader.java:1068)
at java.lang.ClassLoader.loadClass(ClassLoader.java:266)

I seem to have found the cause of the problem.
In my case, I use the Git plugin to receive post commit hooks, those commits have the email of the user that made the changes.
The problem is that the plugin parses the changelog and uses a tries to instantiate the class Mailer$UserProperty which is part of the Mailer plugin.
Previous versions of Jenkins had the Mailer plugin bundled into Jenkins core, now that Mailer is a separate plugin, and Git plugin doesn't specify it as a dependency, it fails.
A quick solution is to install or activate the Mailer plugin, I did that and now all the builds are running perfectly

Federico,

Thanks for that, I have enabled the mailer plugin and that has fixed the issue for me.

Code changed in jenkins
User: Nicolas De Loof
Path:
src/main/java/hudson/plugins/git/GitChangeSet.java
http://jenkins-ci.org/commit/git-plugin/fe92b34775a927fe420d72d5cf8618ed429ee6dd
Log:
[FIXED JENKINS-19345] isolate Mailer-dependent code

We are running exactly into that issue with the git-plugin 2.0.3. But it works with 2.0.1. So there must be a regression bug in 2.0.3. The weird thing is, that we indeed have the mailer plugin installed and still run into that error with git-plugin 2.0.3

FATAL: hudson/tasks/Mailer$UserProperty
java.lang.NoClassDefFoundError: hudson/tasks/Mailer$UserProperty
	at hudson.plugins.git.GitChangeLogParser.parseCommit(GitChangeLogParser.java:80)
	at hudson.plugins.git.GitChangeLogParser.parse(GitChangeLogParser.java:74)
	at hudson.plugins.git.GitChangeLogParser.parse(GitChangeLogParser.java:51)
	at hudson.plugins.git.GitChangeLogParser.parse(GitChangeLogParser.java:29)
	at hudson.model.AbstractBuild.calcChangeSet(AbstractBuild.java:903)
	at hudson.model.AbstractBuild.getChangeSet(AbstractBuild.java:877)
	at hudson.model.AbstractBuild.getCulprits(AbstractBuild.java:413)
	at hudson.model.AbstractBuild.getCulprits(AbstractBuild.java:410)
	at hudson.model.AbstractBuild$AbstractBuildExecution.post(AbstractBuild.java:710)
	at hudson.model.Run.execute(Run.java:1690)
	at hudson.model.FreeStyleBuild.run(FreeStyleBuild.java:46)
	at hudson.model.ResourceController.execute(ResourceController.java:88)
	at hudson.model.Executor.run(Executor.java:246)
Caused by: java.lang.ClassNotFoundException: hudson.tasks.Mailer$UserProperty
	at org.apache.tools.ant.AntClassLoader.findClassInComponents(AntClassLoader.java:1365)
	at org.apache.tools.ant.AntClassLoader.findClass(AntClassLoader.java:1315)
	at org.apache.tools.ant.AntClassLoader.loadClass(AntClassLoader.java:1068)
	at java.lang.ClassLoader.loadClass(ClassLoader.java:358)
	... 13 more

I'm seeing the same problem having just upgraded to Jenkins 1.557. I have version 2.1.0 of the Git plugin, and version 1.8 of the Mailer plugin. Is there a workaround, or versions of the plugins that are known to work together?

I uninstalled and re-installed the Git plugin (suggested elsewhere), which seems to have "fixed" it.

@Graham Hay I tried what you suggested but I still get the same error every time the GIT plugin updates from the origin repo.

Yeah, I still had problems after that too. I've since updated to Jenkins 1.558, and v2.2.0 of the Git plugin; and not seen that error recently. I had a look in the commit log for the plugin, but couldn't see anything that was an obvious fix.

I solve this problem downgrading the git-client and git plugins to 1.9.0 and 1.5.0 respectively, as Berg Systeme suggested in his blog:
http://blog.berg-systeme.de/2014/05/15/downgrade-jenkins-git-plugin/