I've been a baseball fan since 1969 when the "Miracle" Mets bounced my Chicago Cubs from the National League championship. Living in the backwoods of West Virginia, I never saw my Cubs play in person or on TV. Instead, I listened to my beloved Cubs at night on my radio, which was tuned in to WGN. Today, thanks to MLB.TV, I can watch the Cubs, or any other team, anywhere I've got broadband and on almost any device.
MLB.TV takes the various local sports network broadcasts--NESN for the Boston Red Sox, YES for the Yankees and so on-and enables you to watch them over your Internet connection. In my experience, you'll need at least a 768Kbps (Kilobit per second) down connection for Standard Definition (SD) TV, and for High Definition (HD) broadcasts, you'll need at least a 3Mbps (Megabit per second). You'll be happier though with at least 1.5Mbps for SD.
This in turn means that while you can use smartphones and tablets to watch baseball over the Internet, 3G usually isn't going to do the job. Instead, you'll need a high-speed Wi-Fi connection. Indeed, the MLB.com At Bat 11 applications for iPhone, iPod Touch, Android, Blackberry, and iPad doesn't try to give you live video. Instead, it provides a simulated video. You can still use a mobile device's Web browser, if Flash is supported, to 'see' a game, but without 4G, it's not that great. Personally, if I were stuck with using a mobile device most of the time, I'd just subscribe to the Internet radio MLB.COM Gameday Audio service.
While MLB.TV only talks about Windows and Macs, it actually works well, in my experience, on Linux PCs as well. To view HD though you need the free Windows and Mac specific NextDef plug-in.
As for Internet video extender devices, you can use a Sony PS3, the second-generation Apple TV, a Roku or Boxee media player, and, some LG and Samsung Internet-enabled HDTVs and Blu-Ray DVD player.
The one downside to MLB.TV is that you're still stuck with local broadcast blackouts. So, for example, in Asheville, NC, I may not be able to watch all Atlanta Braves or Cincinnati Reds games. That's no skin off my nose, but before buying the service make sure your team isn't subject to local blackouts.
The cost for the service, with all the extras, such as your choice of home and away broadcasts and DVR style controls, is $119.99 for the whole season. It's $99.99 for the basic version. By comparison, DirecTV's MLB Extra Innings is $209.44, and, of course, you have to subscribe to DirecTV. For those of you, like me, who still find just listening to baseball a little bit magical, Gameday Audio is only $19.95 for the whole season.