I'm using Highrise for this example, as that is the CRM I use. But you can quickly modify this for any CRM.
This IVR integration will check your incoming call and see if the phone number exists in your Highrise contacts. If it does, it will add the caller's name to the database record.
You'll need a Highrise account to do this, and you can get one at http://highrisehq.com.
There are two credentials you'll need for this, your account name and your API key.
You can get your account name from the address bar of your browser:
And then, you can find your API key by clicking My Account and then going to API token: