FamilySearch adds Great Britain, War Office Registers, 1772-1935

FamilySearch describes these as "a variety of records ... availability may vary by record type, year, and locality ... may include records from England, Scotland, Wales, and Ireland."
A search yields Name, Event Type, Event Place, Birthplace, Birth County, and a link to an image of the original record.
Only registered LDS members can view the image remotely, others need to be at an LDS Family History Centre or affiliate library.
The 47,992 records are sourced from WO 25 at the (UK) National Archives Kew.
Library and Archives Canada holds microfilm copies of some of the WO 25 volumes relating to regiments that served in Canada. There's a list here.