The import com.google.android.gms cannot be resolved

Another way is to let Eclipse do the import work for you. Hover your mouse over the com.google.android.gms import that can not be resolved and towards the bottom of the popup menu, select the Fix project setup... option as below. Then it'll prompt to import the google play services library. Select that and you should be good to go.

I checked off Google API as project build target.

That is irrelevant, as that is for Maps V1, and you are trying to use Maps V2.

I included .jar file for maps by right-clicking on my project, went to build path and added external archive locating it in my SDK: android-sdk-windows\add-ons\addon_google_apis_google_inc_8\libs\maps

This is doubly wrong.

First, never manually modify the build path in an Android project. If you are doing that, at best, you will crash at runtime, because the JAR you think you put in your project (via the manual build path change) is not in your APK. For an ordinary third-party JAR, put it in the libs/ directory of your project, which will add it to your build path automatically and add its contents to your APK file.

However, Maps V2 is not a JAR. It is an Android library project that contains a JAR. You need the whole library project.

You need to import the android-sdk-windows\add-ons\addon_google_apis_google_inc_8 project into Eclipse, then add it to your app as a reference to an Android library project.