Yes you can! Mopapp can track Downloads and Active Installs for your free and paid apps.

For free apps, you just need to register an Android Market store account, and provide the credentials to access it.

For paid apps, you still need to provide the credentials for an Android Marker account, plus you need to register a Google Checkout store account, and provide your Merchant ID and API Key. Please refer to this article to know more about how to retrieve your Merchant ID and API key.