The APK file is just a zip file with another extension. To remove the signature just unzip it, remove the folder META-INF and zip it again.
but how to sign it again? You can use your own signature or the debug signature used by Android SDK named debug.keystore
You can copy the debug signature from C:\Documents and Settings\\Local Settings\Application Data\Android\
The data of the signature is the following:
* Keystore name: "debug.keystore"
* Keystore password: "android"
* Key alias: "androiddebugkey"
* Key password: "android"
* CN: "CN=Android Debug,O=Android,C=US"
for more details go to http://developer.android.com/guide/publishing/app-signing.html
Now, how to sign the apk again? Use the jarsigner.exe tool, this tool comes with the JDK.
JDKFOLDER\bin\jarsigner.exe -verbose -storepass android -keystore debug.keystore myprogram.apk androiddebugkey
replace myprogram.apk with your own unsigned apk.
Is this useful? Maybe, if you want to modify the build with reverse engineering or something similar, use your imagination.