Evidence uncovered indicates that it is quite likely that there is, or was, a game entitled or code-named Command and Conquer: Arena in development at EALA. There's a lot of speculation going around, but it's important to ground that in facts. I've done some investigation, and here's what I have found.
The game probably would have had or has Full Motion Videos or in-game cinematics, possibly computer-generated. The Third Floor, an LA-based previsualization company, worked on the game, as did Shadowplay Studios, also based in LA. Both companies also worked on Red Alert 3 and Need for Speed, also published by EA. Shadowplay Studio and The Third Floor have a long history of working together on a variety of projects.
The game was likely in development dating back to at least early 2008. Chat records reveal that a Blockbuster survey that dated to at least January 2008 included a question about C&C Arena. Additionally, it is likely that C&C Arena predated Red Alert 3, suggesting that the game is the cancelled quasi-C&C shooter Tiberium. When describing their work for Red Alert 3, The Third Floor writes:
Because of our success on C&C Area [sic], Electronic Arts came back to us with a project that was even more epic. As the much-anticipated next installment of C&C, Red Alert 3 already had a very strong fan base, so the expectations were running high. But utilizing the strengths of both Shadow Play and The Third Floor, we rose to the challenge.
Working closely with world-renowned director Richard Taylor, the cinematics were developed in accordance with his vision. Over 3 minutes of final cinematics were created for in-game cutscenes and marketing materials.
When listing his credits, The Third Floor CEO Chris Edwards lists C&C Arena before C&C Red Alert 3. Finally, when C&C Arena was mentioned on The Third Floor's website, this order was also used.
The following posting was on The Third Floor's website until recently--it has since been taken down. It was uploaded to Photobucket by an anonymous user. In it, you can clearly see the promotional material for C&C Arena used by The Third Floor. The written text reads as follows:
The Third Floor teamed with Shadowplay Studio to take Electronic Arts’ concept of an epic robot battle from previs all the way to final cinematics. The highly detailed world was fleshed out from scratch by The Third Floor and Shadowplay teams.
Parse this carefully. Many are reading this as saying that C&C Arena will be all robots. I do not believe this is accurate. I believe it merely refers to a single cutscene done by The Third Floor and Shadowplay, which perhaps has mostly or only robots. The "from scratch" part only means, I think, that they worked on the scene from nothing, not that it's a whole new universe, as some speculators have suggested.
There is a lot of speculation about the game being made available for free and supported through micropayments. I do not think this is the case. The best I can tell, this rumor dates to a comment by "thisguyinhere" on February 5th, 2008. I can find no corroborating evidence, and lots of evidence that points against it.
Now for my own speculation: I believe this title is a reference to Tiberium, the canceled C&C shooter. The title, content, and timeframe all fit ("Arena" is added to shooter titles on occasion, such as Quake 3: Arena). I believe these two companies did previsualization work for the game before it was canceled.
I believe that we'll see a non-RTS C&C at some point, maybe even with this name, but what we have seen here isn't it.