They're basically been slaughtered by the likes of Netflix--to the extent that BB tried to sue them out of existence!
It's all a little funny really. While Netflix was still struggling through its growing pains, they went to Blockbuster trying to sell out; Blockbuster turned down the deal thinking that the Netflix model would never go anywhere.
http://www.hackingnetflix.com/2005/10/variety_blockbu.html
http://www.slate.com/id/2133995/Variety has an excellent analysis of the troubles that Blockbuster is facing in the story "Blockbusted!" In the article a former Blockbuster executive is quoted as saying:“We had the option to buy Netflix for$50 million and we didn't do it. They were losing money. They came around a few times," he recalls. Instead, in 2000, Blockbuster inked a 20-year exclusive video-on-demand pact with Enron as the energy conglom launched into telecom. Blockbuster canned the pact after nine months. Netflix is now worth $1.4 billion. Blockbuster’s market cap is about $850 million.
Also note that this article is from 2005. BBI's market cap is now $122 million while Netflix's is $3.24 BILLION. Stick a fork in Blockbuster--they're done.