Battletech is alive and kicking.
Currently produces by Catalysm game labs, and officially going by the moniker "Classic Battletech" (something forced on them during the dark days of clickytech, and kept just out of inertia) Their current website can be seen here: http://www.classicbattletech.com/
There are currently 4 core rule books in print that I'm aware of. "Total Warfare" is the core book, and all you really need to play. (apart from maps, recordsheets, and some kind of counters for mechs) Second book is "Techmanual", this has all the construction rules for everything from conventional infantry up to and including dropships. (Aerospace craft have been rolled into the core rules now) Third is "Tactical Operations" which is the "Maximum Tech" advanced rules book, for the most part. Experimental equipment, optional rules, that kind of thing. The last is "Strategic Operations" which includes rules for warship combat and construction, as well as a campaign rule set. Looking at their website it does appear that the fifth book "A Time of War" has gone to print (though I've yet to see it in person) this is the new version of the Mechwarrior RPG. (quickstart version of the rules available here: http://www.classicbattletech.com/index. ... #downloads
Timeline wise the story's up to about 3080, the most recently published TRO is 3085, and the most "up to date" fluff book is "Jihad Hot Spots: Terra". They've also done a number of "Historicals" covering events such as the War of '39 and Operation Klondike.
If you're the nostalgic type the Unseen made a re-emergence about 5 years ago as the "reseen" with all new artwork, fluffed out as "updated designs". They also actually got the rights to all of the unseen that didn't originally come from Macross, (Griffin, Goliath, Battlemaster, Locust, Thunderbolt, etc) and are able to use that artwork again, though all it's really meant is that further "updates" to the reseen have gotten closer to the original looks of the designs. (and that a few older books have become available in PDF that much quicker)
Miniatures wise battletech's doing well, with new minis released as recently as September. I understand the owner of the company making the minis (Iron Winds Metals) has had a bit of an emergency recently, so production has slowed, but they have been releasing new minis pretty much every month.
"When people play" will vary wildly depending on who you talk to. Some people want the cutting edge of the timeline and play in 3080, others abhor the clans and still play 3025. Some people (such as myself) don't actually care and will play whatever I feel like/my opponent will agree to. (my preference is 3050s as my prime allegiance is to Clan Ice Hellion)