Thank you everyone for the feedback! As a first step, we are now working on a functionality to persist your last state on report pages in the Power BI service. This will essentially remember all your filter and slicer states, so you don’t have to re-select everything once you navigate away or refresh the page. We will continue to build on this and add more functionalities (such as saving various filter combinations via. bookmarks) in the near future.
Hey all - we're planning on GAing this feature in the upcoming weeks. We're going through final rounds of testing.
If you haven't read the latest feature summary from the February Desktop release, we added a option for authors to disable this feature (if needed) for their reports before it hits the service: https://powerbi.microsoft.com/en-us/blog/power-bi-desktop-february-2018-feature-summary/#persistentFilters