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.
Ariane 5 went expendable specifically to make it feasible to build, where Sanger and similar SSTO re-usable spaceplanes were too far-fetched to build.
The EELV and Ariane were a reasonable approach at the time to make rockets a bit more affordable. Any way to do reusability at the time would have required a novel and exotic architecture, with a matching exotic budget. And that just wasn't in the cards.
But now it's not that impossible or expensive to ask a rocket stage to drop out of the sky and sit on its tail. (The hovering rocket is a garage project at this point, though a difficult one--but mostly because of the "rocket" part and not the "hovering" part.) Any existing stage could be modified to do the same with modern avionics, with the addition of an RCS and restartable engine (if it doesn't already have those). Sure, SpaceX's choice of 9 throttlable engines makes it easier, but you can do the "hover-slam" with just one giant one.
Any incumbent who can't manage to do so will rightly be done within a decade. And as hide-bound as they all seem to be, that might be most of them. They'll still have to deal with SpaceX's manufacturing efficiency, which might be even harder, as manufacturing inefficiency is part, for example, of Ariane's DNA. But at least they'll stay in the race.
After stage separation, it detach the entire engine block (where most of the cost is), and a helicopter captures the parachute mid-flight! (See figure 2 from the PDF)
Airbus wanted to use SpaceX but the French flipped out so they have to stick with Ariane.
You see, there are two ways to build reusable rockets. One way is to build a purely reusable vehicle from the ground up, but this is extraordinarily expensive because of all the testing involved before it can be used commercial. The other is to build an expendable/reusable hybrid. A rocket that can be used in an expendable configuration but has all of the needed elements to allow for reusability down the road. This is vastly easier because it means you can bootstrap development on the back of commercial launch business, and do testing that is largely subsidized by paying customers. And this is what SpaceX has been doing.
However, there's a problem. You have to head into reusability from the get go, you can't just modify any old rocket for reusability, you need to design from a place of suitability for reuse from square one. And while that's not an enormous difficulty it is very much non-trivial, and imposes a substantial overhead on R&D and manufacturing costs. This is because most of the optimizations for building a purely expendable rocket drive the design away from the optimizations you'd want for a reusable rocket. In an expendable design it's common for there to be a mix of propellants and a diversity of engine designs between the first and upper stages, it's also common for the upper stage to be more expensive than the first stage, because that stage is more critical for payload performance and launch precision. Also, it's common to minimize the number of engines on the first stage. Even the Saturn V had only 5 first stage engines. And generally there'd be no reason to add first stage engine restart capability on an expendable vehicle.
All of those things results in an expendable vehicle that is completely unsuited to reuse. It leads to a first stage that is very difficult to modify for reuse, and an overall rocket design that does not reward the easiest type of reuse (of the first stage) because most of the cost is in the upper stage anyway. SpaceX went to a great deal of effort to ensure that they built a rocket that could serve the expendable launch market immediately (and pull in hundreds of millions of dollars in revenue) while also being suitable for reuse with comparably moderate modifications. The first stage has 9 engines, so throttling down to a thrust level suitable for precision landings of a mostly empty stage is possible by using only one engine. The first stage use restartable engines (using onboard TEA/TEB igniters). And the first stage is about 3/4 of the hardware cost of the vehicle, since the 2nd stage uses only one engine and is also LOX/Kerosene fueled.
That foresight has allowed SpaceX to be in the launch business for several years, proving the capability of the company and gaining much needed experience in building and flying rockets while also poising the company to bring to market a reusable launcher. In comparison, every other established launch provider in the world could only do reusability by designing a new launcher from scratch.