Sweden, which has had less COVID-19 restrictions than many countries, still uses a COVID-19 vaccine pass for travelling, attending indoor events and public gatherings.
--- see below for update per February 9 --
Currently, February 2, a set of rules are in effect. They have changed several times over the last two years and are expected to change in the near future.
For travel inside Sweden
Inside Sweden there are and has been no requirements for covid pass.
For travel to Sweden
For travel to Sweden (passing the border) there is a general prohibition but it differs between Swedish citizens (and certain others) which currently does not need covid pass but may need to show negative test, and citizens of countries outside EEA depending on from which country they arrive from.
Third country nationals (non-EU/EEA*) needs to be covered by an exemption in order to enter. More information about exemptions can be found on the entry page for third country nationals.
Entry from a non-EEA* country : Must be covered by at least one exemption to the general entry ban (e.g. reside in an exempted country) or be fully vaccinated and hold a vaccine certificate from a so called approved country.
If covered by an exemption, need to present a valid covid certificate.
Swedish Police (notice, this is expected to change)
And I must confess, I cannot really understand what the rules are. But in some cases you need a covid pass to enter Sweden, in some cases not.
For travel from Sweden
There are no restrictions on leaving Sweden. (Sidenote: all air lines enforce the rules of the country you are going to, but there are no other restrictions imposed by Swedish authorities. )
Attending indoor events and public gatherings
Yes, you quite often need a covid pass.
At public gatherings and public events with more than 50 participants indoors, vaccination certificates must be used, together with assigned seats, and a distance of one meter must be kept between parties.
Crisis information (expected to change)
--- Update per February 9 ---
All restrictions inside Sweden has now been lifted and only recommendations remain.
The general travel restrictions are no longer in effect except for travel to Sweden from "third countries" which will then require covid passport, currently planned to be lifted March 31. If you plan to travel, do check actual and current situation as it might change at short notice.