Depends on the robot. No remains of our 2008 and 2009 robots exist. Stripped-out frames of the 2010, 2011, and 2013 robots remain, although they have no electronics or mechanisms.
Our 2012 robot is still functional, although it's been through some
abuse modifications. It's great for outreach, and although it was pretty bad at its own game, it's got a mean cleat shot if you can get it over a defense.
The 2014 bot is in need of extensive repairs, after destroying its own pull-back mechanism at an outreach event (nobody was hurt). However, its powertrain is still in good shape, so we use it for driver practice and
prototype shenanigans. The yoga ball makes for great crowd interaction, when there's enough room. The clone practice bot has been stripped down to the chassis and is also used for prototyping.
The 2015 robot is still in near-perfect condition, and we plan on keeping it that way indefinitely. The roborio has been removed for this year's practice bot, but the rest of it remains. The practice robot was kept around briefly for a stint at R2OC as team 8338, but has since been fully disassembled.
The 2016 practice robot is currently in about 100 different pieces after being cannibalized for champs, and we are likely to keep the competition robot around for outreach, as it's very portable, relatively safe, and has a great chassis for the outdoors.
Side note- Last I knew, 1625 still had their 2006 robot fully functional, and used it as a defense bot for some pre-bag and tag practice in 2014. Anyone know if that thing is still around? It certainly deserves a nod among historic FRC robots that are still functional.