There have been many video-games based on the show, spanning the Game Boy Advance and the Playstation. However, as is the case with many video games based on licensed properties these games have been critically panned. There are also some web based games you can play on the internet for free. For example you can play some flash games on this website: beyblade-games.net
History
The first Beyblade related toys were released in 1999, but they were also accomplied by the first Beyblade video game Jisedai Bēgoma Battle Beyblade. This featured many protype ideas and concepts that were never implimented into the full release of the Beyblade series.
Later in 2000, a manga was released, defining the "canon" Beyblade storyline. Often, as was the case, the video games were released based on the limited storyline and toys that were know at the time and so have often substituted or improvised many elements of the beyblade franchise. Each video game is therefore not official canon, though often based on the current known storyline of Beyblade.
Releases
See here for more information.