If you have the source code of your project you can build it without Eclipse, signing an unsigned apk can be also achieved using ant
Here is a quick tutorial on how to build signed APK without Eclipse.
Type in to CMD
cd your/project/folder/
android update project -p .
Add to project.properties the following settings:
key.store=path/to/export/key
key.alias=alias_name
key.store.password=store_password
key.alias.password=alias_password
Type in to CMD
cd your/project/folder/
ant relese
The output APK will be found in the bin folder
Note: that this requires android SDK installed.
if you get the following error:
'android' is not recognized as an internal or external command
'ant' is not recognized as an internal or external command
You should add your android-sdk/tools and android-sdk/platform-tools to system path, here is a tutorial on how to do it:
http://geekswithblogs.net/renso/archive/2009/10/21/how-to-set-the-windows-path-in-windows-7.aspx