SpaceX is first with inter-satellite laser links in low-Earth orbit, but others will follow.

SpaceX is willing to subsidize expensive hardware like laser links and end-user terminals in the short run.

When SpaceX first announced plans for Starlink, their low-Earth orbit Internet service constellation, they said each satellite would have five inter-satellite laser links (ISLLs) -- two links to satellites in the same orbital plane, two to satellites in adjacent orbital planes, and one to a satellite in a crossing plane. They subsequently dropped the crossing link as too difficult and, when they finally began launching satellites, they had no laser links. Last year they tested ISLLs on two satellites.

Last November, SpaceX requested that the FCC modify its license to allow them to operate 348 satellites at an altitude of 560 km and an inclination of 97.6 degrees in order to serve the polar regions. This month, the FCC postponed their decision on the 348 satellites, but granted SpaceX permission to operate ten satellites to "facilitate the continued development and testing of SpaceX’s broadband service in high latitude geographic areas" and those ten satellites were launched as part of a 143-satellite rideshare.

That rideshare was a record-setter, but it is more interesting to note that those ten polar-orbit satellites were equipped with operational ISLLs and Elon Musk confirmed that the remaining 338 would also have ISLLs if approved. In the same tweet, he confirmed that their inclined-orbit satellites would be equipped with ISLLs next year, but only the polar satellites would have them this year.

SpaceX must be confident that the full 348 satellites will be authorized since the first ten, while useful for tests, would not provide meaningful connectivity and my guess is that the polar-orbit satellites will be able to link to the inclined-orbit satellites with lasers when they begin launching next year. (Note that Telesat has applied for a patent on a Dual LEO Satellite System in which polar and inclined-orbit satellites communicate with each other).

How about the other LEO satellite projects?

Telesat plans to launch a hybrid constellation with laser links connecting polar and inclined satellites and is already working with Mynaric, a German laser communication company, on Blackjack, a LEO constellation being developed for the US Department of Defense, so Mynaric may supply the lasers for Telesat's satellites. It's also interesting that Mynaric's US office is in Hawthorne, California, home of SpaceX. OneWeb initially planned to equip their satellites with ISLLs, but they decided not to for cost and political reasons. As far as I know, Jeff Bezos' Project Kuiper has not officially committed to having ISLLs between their satellites, but they are hiring optical engineers to work on the constellation and are planning applications that will benefit from ISLLs. I don't know about the Chinese broadband LEO companies, but at least one Chinese company Intane, produces space lasers. (Mynaric has withdrawn from the Chinese market due to political pressure).

HydRON connecting the ground,
LEO and GEO satellites and deep space

In the long run, I expect that every LEO broadband provider that survives, will be linking their satellites with ISLLs -- doing so will lower latency and reduce the need for terrestrial ground stations. Furthermore, I expect we will see ISLLs between LEO, MEO and GEO satellites. Telesat and OneWeb may have the lead on multi-layer links since Telesat is already a well-established GEO satellite communication company and Hughes is an investor in OneWeb. SES, which operates both MEO and GEO satellites is an investor in the forthcoming European Union LEO constellation and the European Space Agency has a long ISLL history and has recently launched project HydRON, which hopes to demonstrate the seamless extension of terrestrial fiber networks with "fiber in the sky" -- a terabit GEO/LEO optical network in space

But, that's the long run. For now, SpaceX is far ahead of the field in nearly every dimension, including ISLL development and deployment and it seems they are willing to subsidize expensive hardware like laser links and end-user terminals while focusing on relatively affluent markets like North America, Europe, and Australia in the short run.

Update 10/25/2020

Here are two more reasons why every successful LEO constellation operator will have inter-satellite laser links (ISLLs). Constellations with ISLLs will be able to offload traffic from the orbital network to terrestrial gateways on islands in the middle of an ocean or other low-utilization locations and the operators will not have to obtain gateway spectrum licenses in nations where the regulators balk. (Pointed out by @Megaconstellati and @trengriffin).

Update 9/30/2022

Starlink has activated the laser terminals on their version 1.5 polar orbit satellites. An early user reports that he is getting intermittent connectivity and high speeds (since he is the only one up there). Uptime should improve as more polar-orbit satellites are launched. I wonder about latency.

https://old.reddit.com/r/Starlink/comments/xr3ali/update_snowy_owl_helped_dishy_do_a_speed_test_at/