From the mid 80's a lot of astronauts but also kosmonauts started using quartz digital watches. Probably the first digital watches that were used in space were soviet watches Elektronika. Since I don't know which of the Elektronika models were in fact used in space, I will not present Elektronika watches here (even though I have two models and you can see them in the soviet section).

The real boom of digital watches in space were made by Casio G-Shock models. They were used in Skylab missions, in ISS space stations and they were used by NASA and Roskosmos flights. As I know G-shock watches were even certified by NASA, but still they were not official NASA watches. 

From G-shock series at least the following models were used in space:   DW-5600C; DW-5600E, DW-5900 C-1; DW-6900. 

I have only DW-5600E new edition. I must admit I am not fan of digital watches so I have just this model to cover G-shock.

In space also Seiko digital watches were worn, at least some of the models from Seiko Sport 100 series, which were used in Skylab and ISS. I have this version.

Very important brand in this respect is also Timex. Watches from the Timex Datalink series were used quite often in the missions in 90's. As I know also  Timex Datalink was certified by NASA. Model 78401 were used by at least Daniel T. Barry on STS-72 Space Shuttle, kosmonaut Sergej K. Kirkaljev on ISS and  Maxim Surajev on Expedition 22 mission.  Model 70502 was worn by James H. Newman on STS-88, model Datalink USB by Daniel Tani on Expedition 16, model Datalink 150 by William Sheppard on Expedition 1 mission, Mihail Tjurin on Expedition 14, Jurij Gidzenko on Expedition 1. I own Datalink 150 in new condition.