You're unable to run Jenkins on the raspberry pi with the new Java JDK 8 for ARM (http://jdk8.java.net/fxarmpreview/). Although the JDK is still in 'early access' it shows that Jenkins is still using non-standard Java classes such as sun.security.util.DerValue.

Jenkins was installed by adding the following line to /etc/apt/sources.list:
deb http://pkg.jenkins-ci.org/debian binary/

• sudo apt-get update
• sudo apt-get install jenkins

In /var/log/jenkins/jenkins.log appears the following stacktrace:

Running from: /usr/share/jenkins/jenkins.war
25 Feb 2013 18:47:34 winstone.Logger logInternal
INFO: Beginning extraction from war file
25 Feb 2013 18:48:33 hudson.WebAppMain contextInitialized
SEVERE: Failed to initialize Jenkins
java.lang.ExceptionInInitializerError
at java.lang.Class.initializeClass(libgcj.so.13)
at hudson.WebAppMain.installLogger(WebAppMain.java:253)
at hudson.WebAppMain.contextInitialized(WebAppMain.java:104)
at winstone.WebAppConfiguration.<init>(WebAppConfiguration.java:876)
at winstone.HostConfiguration.initWebApp(HostConfiguration.java:129)
at winstone.HostConfiguration.<init>(HostConfiguration.java:71)
at winstone.HostGroup.initHost(HostGroup.java:87)
at winstone.HostGroup.<init>(HostGroup.java:47)
at winstone.Launcher.<init>(Launcher.java:177)
at winstone.Launcher.main(Launcher.java:384)
at java.lang.reflect.Method.invoke(libgcj.so.13)
at Main._main(Main.java:273)
at Main.main(Main.java:98)
Caused by: java.lang.NullPointerException
at com.thoughtworks.xstream.core.JVM.isOpenJDK(JVM.java:72)
at com.thoughtworks.xstream.core.JVM.canUseSun14ReflectionProvider(JVM.java:198)
at com.thoughtworks.xstream.core.JVM.bestReflectionProvider(JVM.java:175)
at com.thoughtworks.xstream.XStream.<init>(XStream.java:431)
at com.thoughtworks.xstream.XStream.<init>(XStream.java:385)
at com.thoughtworks.xstream.XStream.<init>(XStream.java:323)
at hudson.util.XStream2.<init>(XStream2.java:79)
at jenkins.model.Jenkins.<clinit>(Jenkins.java:3798)
at java.lang.Class.initializeClass(libgcj.so.13)
at hudson.WebAppMain.installLogger(WebAppMain.java:253)
at hudson.WebAppMain.contextInitialized(WebAppMain.java:104)
at winstone.WebAppConfiguration.<init>(WebAppConfiguration.java:876)
at winstone.HostConfiguration.initWebApp(HostConfiguration.java:129)
at winstone.HostConfiguration.<init>(HostConfiguration.java:71)
25 Feb 2013 18:48:36 winstone.Logger logInternal
SEVERE: Error during context startup for webapp webapp
java.lang.ExceptionInInitializerError
at java.lang.Class.initializeClass(libgcj.so.13)
at hudson.WebAppMain.installLogger(WebAppMain.java:253)
at hudson.WebAppMain.contextInitialized(WebAppMain.java:104)
at winstone.WebAppConfiguration.<init>(WebAppConfiguration.java:876)
at winstone.HostConfiguration.initWebApp(HostConfiguration.java:129)
at winstone.HostConfiguration.<init>(HostConfiguration.java:71)
at winstone.HostGroup.initHost(HostGroup.java:87)
at winstone.HostGroup.<init>(HostGroup.java:47)
at winstone.Launcher.<init>(Launcher.java:177)
at winstone.Launcher.main(Launcher.java:384)
at java.lang.reflect.Method.invoke(libgcj.so.13)
at Main._main(Main.java:273)
at Main.main(Main.java:98)
Caused by: java.lang.NullPointerException
at com.thoughtworks.xstream.core.JVM.isOpenJDK(JVM.java:72)
at com.thoughtworks.xstream.core.JVM.canUseSun14ReflectionProvider(JVM.java:198)
at com.thoughtworks.xstream.core.JVM.bestReflectionProvider(JVM.java:175)
at com.thoughtworks.xstream.XStream.<init>(XStream.java:431)
at com.thoughtworks.xstream.XStream.<init>(XStream.java:385)
at com.thoughtworks.xstream.XStream.<init>(XStream.java:323)
at hudson.util.XStream2.<init>(XStream2.java:79)
at jenkins.model.Jenkins.<clinit>(Jenkins.java:3798)
at java.lang.Class.initializeClass(libgcj.so.13)
at hudson.WebAppMain.installLogger(WebAppMain.java:253)
at hudson.WebAppMain.contextInitialized(WebAppMain.java:104)
at winstone.WebAppConfiguration.<init>(WebAppConfiguration.java:876)
at winstone.HostConfiguration.initWebApp(HostConfiguration.java:129)
at winstone.HostConfiguration.<init>(HostConfiguration.java:71)
25 Feb 2013 18:48:36 winstone.Logger logInternal
INFO: HTTP Listener started: port=8080
25 Feb 2013 18:48:36 winstone.Logger logInternal
SEVERE: Error during servlet context shutdown
java.lang.NoClassDefFoundError: jenkins.model.Jenkins
at java.lang.Class.initializeClass(libgcj.so.13)
at hudson.WebAppMain.contextDestroyed(WebAppMain.java:336)
at winstone.WebAppConfiguration.destroy(WebAppConfiguration.java:1167)
at winstone.HostConfiguration.destroyWebApp(HostConfiguration.java:148)
at winstone.HostConfiguration.destroy(HostConfiguration.java:156)
at winstone.HostGroup.destroy(HostGroup.java:77)
at winstone.Launcher.shutdown(Launcher.java:337)
at winstone.Launcher.<init>(Launcher.java:199)
at winstone.Launcher.main(Launcher.java:384)
at java.lang.reflect.Method.invoke(libgcj.so.13)
at Main._main(Main.java:273)
at Main.main(Main.java:98)
25 Feb 2013 18:48:36 winstone.Logger logInternal
INFO: Winstone shutdown successfully
25 Feb 2013 18:48:36 winstone.Logger logInternal
SEVERE: Container startup failed
java.io.IOException: Failed to start a listener: winstone.ssl.HttpsListener
at winstone.Launcher.spawnListener(Launcher.java:229)
at winstone.Launcher.<init>(Launcher.java:185)
at winstone.Launcher.main(Launcher.java:384)
at java.lang.reflect.Method.invoke(libgcj.so.13)
at Main._main(Main.java:273)
at Main.main(Main.java:98)
Caused by: java.lang.NoClassDefFoundError: winstone.ssl.HttpsListener
at java.lang.Class.initializeClass(libgcj.so.13)
at java.lang.Class.forName(libgcj.so.13)
at winstone.Launcher.spawnListener(Launcher.java:213)
...5 more
Caused by: java.lang.ClassNotFoundException: sun.security.util.DerValue not found in java.net.URLClassLoader{urls=file:/tmp/winstonemwgzajjar, parent=gnu.gcj.runtime.SystemClassLoader{urls=file:/usr/share/jenkins/jenkins.war, parent=gnu.gcj.runtime.ExtensionClassLoader

}}
at java.net.URLClassLoader.findClass(libgcj.so.13)
at java.lang.ClassLoader.loadClass(libgcj.so.13)
at java.lang.ClassLoader.loadClass(libgcj.so.13)
at java.lang.Class.initializeClass(libgcj.so.13)
...7 more