Android Studio could not find any version that matches com.android.support:appcompat-v7:23.+

Change all the dependencies with the package name com.android.support: version from 23 to 22.2.1 or 22.+ then sync Gradle.

This will fix it till they update the support libraries.

Example

dependencies {
    // compile `com.android.support:appcompat-v7:23.+`
    compile `com.android.support:appcompat-v7:22.2.1`
}

Update August 18th, 2015: couple hours later

Android Support 23 is available now. You can now restore your dependencies back as they were before and download the two below using the Android Studio SDK manager:

Support Repository 17

Android Support Library 23.0.0

I've been dealing with this too. It looks like they updated Android Studio to use appcompat v7:23 as a default even though it hasn't been released yet.

Make sure you have downloaded Android Support Repository (not only Android Support Library) - launch the SDK Manager (from your android-sdk location, on Windows must be as administrator, otherwise it might not connect) and look in the Extras section if you have both these components installed (I'm assuming you already have the Android SDK of the desired API level). Restart your IDE and it should work.