It very much depends on what you mean by obsolete, especially from the point of view of what you are learning. Even when SQL Server 2008 (and 2008r2) drop out of their extended support windows (as 2005 will do next year) a lot of what you are learning is almost certainly still going to be relevant to 2012/2014/2016 especially if you are learning from a beginner level: building tables is much the same,
SELECTing data too, even with the more advanced options like CTEs and XML output, views, stored procedures, triggers, and so forth also.
It is worth having a clue of what was added in the other versions of course, while the core is the same there were additions like 2012 adding support for more windowed functions (like
LEAD and some other related syntax - I'd love to use those for some reports but can't as some of our client installs are still 2008r2).
From a DBA point of view things are more different: changes in mirroring, clustering, always-on and friends have been significant in places through the versions from 2008 to 2016 for example, and then there are differences in 2014 between the local editions and the azure variety. But still, a lot of stuff is pretty much the same so learning 2008 will still not be a complete waste of time by any stretch of the imagination.