If a plugin upgrade causes problems, Jenkins may not restart. You'll be welcomed by an error message and a stack trace. Don't panic! Go into your Jenkins plugin directory, list files by date, and then disable the most recent ones:
$ cd $JENKINS_HOME/plugins
$ ls -ltr *.jpi
-rw-r--r--. 1 root root 169194 Feb 22 10:12 script-security.jpi
-rw-r--r--. 1 root root 516115 Feb 22 10:12 next-executions.jpi
-rw-r--r--. 1 root root 739004 Feb 22 10:12 email-ext.jpi
$ touch email-ext.jpi.disabled next-executions.jpi.disabled script-security.jpi.disabled
$ service jenkins restart
Files ending in .disabled
instruct Jenkins to disable the corresponding plugin. Delete the disabling files until you've found the offending plugin. Then you can go into Jenkins and revert it to an earlier version.
Word of advice: Upgrade plugins in small batches. Doing so helps you isolate early problematic plugins.