You do not need an API Key to use Goolge Maps API V3. However, we just experienced an issue where Google reported that we had exceeded our limit, even though we didn't (Development Server). I went ahead and set up an API Key, and its actually beneficial, because you then get usage reporting. Also, we haven't seen the false Quota usage problem since then. I thought I would go ahead a share the process:
Goto https://console.developers.google.com/
Click the red 'Create Project' button
Give your project a name and Google will automatically give it an ID
Wait until the Spinny on the bottom says your project is complete.
In the left hand nav, select APIs Under APIs & Auth, and select 'Google Maps JavaScript API v3'

Click the link and then Turn on the API


Go to Credentials under the APIs & Auth section, and click the red 'Create New Key' under the Public API access section. Then click Browser Key.

Make sure you include the star in your Website's name. For example, use mywebsite.com/*. This will ensure all pages are authorized to use the API.
Copy the key into your Javascript reference to the Google Maps API, like so:
<script type="text/javascript" src="https://maps.googleapis.com/maps/api/js?key=YOUR_KEY"></script>

Long story short, the key is not required, but best practices would indicate that you should use the key.