Research in Motion is planning to show off its own rival to the Apple App Store today at the CTIA trade show in Las Vegas today.

The new BlackBerry App World, which has been touted for some time, is one of many copycats that hope to steal Apple’s sizzle. Co-chief executive Mike Lazaridis will unveil the store at his keynote speech. Other rivals unveiling stores soon: Nokia, Google, Microsoft and Palm.

You need to have a PayPal account, a trackball, the 4.2 version of the operating system or higher, or SurePress touch screen (available on models such as the BlackBerry Storm). To get to the store, you need to download the storefront to your phone.

The store’s home page has featured items which you can navigate by scrolling sideways. You can click on tabs that allow you to search by types of apps such as games, music, video, and health. You can also download apps based on their popularity rankings. When you buy something, you activate the PayPal payment system to close the purchase.

Featured apps include Yahoo Messenger, Bloomberg, Facebook, MySpace, AOL Instant Messenger, and Google Talk. All of those apps are free. Scores of apps are already available. CrunchGear has a full list.