Good question person from 2017.
Ok. Listen to this song while reading this if you want.
Ok, I'm going to define SpaceX competitors as any launch vehicle, which is a loose definition, but this can just be the summary of every RLV in development. I don't have price points for any of these; which is probably the most important factor, but eh.
US commercial companies:
Primary competitor to SpaceX, let's take a look.
Blue Origin New Glenn: VTVL reusable first stage LV capable of 45 tons to LEO. Currently aiming at NET Q4 2022 for first launch.
ULA Vulcan: Developing SMART reuse for Vulcan (27 tons to LEO (maybe more)) where the engine section and boosters seperate from the main booster, reenter using an inflatable heat shield, deploy a parachute and are caught with a helicopter. They are also developing the Centaur V to become an in space reusable stage, where they refuel in space. There's been proposals for recovery Centaur V with SMART and flyback boosters, but that's not on the board right now. Aiming at October, though it's unclear on the timeline for when SMART will be integrated.
ACES has now been cannibalised into Centaur V
Rocket Lab Neutron: VTVL reusable first stage LV capable of 8 tons to LEO. NET launch date of 2024.
Relativity Space Terran R: Fully reusable launch vehicle capable of 20 tons to LEO. Presumably VTVL first stage; but unclear on second stage. No current NET launch date.
Rocket Lab Electron: Smaller launcher capable of ~300kg to LEO and is already launching. They are using a similar approach to SMART to recover the first stage, with first booster reflight aimed at 2022
That's the main US RLV in development. But launch is a worldwide thing.
Arianespace Ariane Next: The specifics of this launch vehicle are still very much up in the design space (they haven't on whether they use hydrolox or methalox for first stage and second stage), but it generally has a VTVL first stage. NET launch date of ~2030 with capabilities similar to that of Ariane 6.
Ooo but what about China. Ignoring historical reuse with Chinese characteristics, there are also a lot of current Chinese launchers looking to integrate or be reusable.
Firstly the state is aiming to make some launchers reusable by 2025.
CALT Long March 8R: The most well known of Chinese RLV plans. LEO payload estimate of 5320kg (7600kg*70%). NET launch date of 2023 maybe(?). They'll be building a hopper this year but we haven't heard much more about the timeline than that. The boosters stay attached to minimise debris, decrease cost and increase dry mass when landing. YF-100s will probably have to modified a bit to allow for deeper throttling
SAST Long March 6X Despite conceptually using the same core stage as the CZ-8R, because it's made by a different SOE, it isn't the same. To achieve reuse they're adding 2 YF-115 to the first stage to enable propulsive landing as the YF-100's can't throttle low enough. The NET launch date when announced back in 2019 was 2021, however we haven't heard much about it since; so that's probably slipped. With the launch of the CZ-6A this year, we might hear more about it. It's capable of 1.5 tons to LEO.
CALT Long March 7 is also planned to have reusability implemented. The first stage has a lot more commonality with the CZ-8R then the CZ-6X does, so it should be easier to implement once CZ-8R is launching. Also note that like CZ-8R, the CZ-7A boosters don't seperate from the core stage; which was debris reasons; but also helps with reuse.
But there are also a lot of Chinese commercial launch providers with stated plans. We'll only cover two of the more serious ones though.
iSpace Hyberbola 2. Methalox 2 stage LV with first stage VTVL reusable capable of 1.5 tons to LEO. They're supposed to be building a hopper and launching orbitally this year, but I think the orbital launch especially is liable to slip to 2022.
Galactic Energy Pallas-1: Kerolox 2 stage LV with first stage VTVL reusable capable of 4 tons to LEO. Currently aiming a NET launch date of late 2022.
JAXA announced a roadmap for their reusable launch vehicles. The Falcon 9 eske (VTVL first stage, expendable second stage) family will be first launching in 2030. The reusable single core will be able to put 15 tons into LEO and the reusable tri core will be able to put 26 tons into LEO. Currently studying whether to use hydrolox or methalox for the stages (ring abell), though by 2040 they will have migrated to methalox. A reusable upper stage will be developed for launch in 2040.
ISRO also have plans for a RLV(s). They are working on developing a space plane as well as a modular HLV with a reusable first stage booster. Maybe NET 2023, for this stuff, unsure.
Last and definitely least is Roscosmos with their latest paper rocket with Amur "launching" in NET 2026.
There are probably other proposals, but I'm limiting myself to semi-serious stuff. (sorry, but Firefly Aerospace's Gamma ain't getting on the list) (and like a commercial European reusable SLV probably exists, but at this stage I'm tired)