Ariane 6 seems to be in response to the SpaceX challenge, at least; they aim to halve the cost per kg through cheaper and common upper/lower stage components. Which is good, but still not competitive with F9, much less a reusable version. At one point they almost made it all-solids in the first two stages, plus boosters, which would have totally doomed any future attempts at re-usability. The final design uses a F9-style common component liquid core, so they could maybe do the same thing as SpaceX later. They are still stuck with solid boosters, though, in a pork-provision move for Italy.
I've got to imagine that ULA is quietly looking into it. But it's quite possible they're just hoping SpaceX will eventually implode of its own internal contradictions and they can go back to their nice little government-launch monopoly. Or maybe they've decided they can't do it without absurd expense, based on their internal development costs. Or maybe they just hope to coast on their existing contracts for a while, and deal with it later once SpaceX has taken all the lumps.
NASA, via SLS, sure isn't looking at re-usability anymore. Lower cost to orbit via research should be their main task, if you ask me, but Congress would rather have them fly giant rockets a couple times a decade, apparently.
The Russians, well, are not much into changing things up. (They've been running Soyuz and Proton, their current launch families, since the sixties!) And their recent aerospace development programs have been less than impressive. But they have a real industry to protect, so one would hope they have a strategy.
I think that everyone's waiting for SpaceX to make it work, and then they'll get to copying. My long-term guess is that this'll kill several of the incumbents, a few will make the transition eventually, but most of SpaceX's competition will come from new entrants. In the meantime, SpaceX will be free to reap the profit from the margin between what it costs them and what their old-fashioned competitors can do. And/or capture the whole darn market. And/or grow it with lower prices. Maybe all of the above.