I looked all over the net and the best I can tell is that Budweiser started sponsoring Junior Johnson's cars in 1983. Those cars were the #11 and #12. Darrrell Waltrip won the 1985 championship in the #11. The sponsorship remained with Johnson's effort through Bill Elliot's tenure that ended when he started his won team for the 1995 season.
Bud moved to Hendrick Motorsports in 1995. As GTR said the #25 has been with Hendrick since they started out. Tim Richmond was the first driver for the Hendrick team. He drove the car in 1986 and 1987. He sat out part of the 87 season because of his failing health. Benny Parsons and Rick Hendrick drove the car in the interim.
Ken Schrader drove the car from 1988 to 1996. I remember hearing an interview with Ken Schrader on MRN when his team got the Budweiser sponsorship. He said it was a whole lot easier to get his team to work because they had free beer!
Craven took over in 1997 and was injured in a crash at Texas. Jack Sprague and Todd Bodine filled in. Wally Dallenbach and Randy LaJoie filled in for Craven for some races in 1998. Dallenbach became the full time driver in 1998 when Craven was diagnosed with post concussion syndrome and could not return to racing full-time. In an advertising campaign honoring NASCAR's 50th season, Hendrick and Budweiser renumbered the car #50 for the 1998 season.
Budweiser left the team in 1999 to become the sponsor of the #8 DEI car that Dale Earnhardt, Jr. drives. Jerry Nadeau took over in 1999 and remained with the team until he left the team prior to the Coca-Cola 600 in 2002. Joe Nemichek drove the #25 until he was replaced by Brian Vickers in 2004.
As we all know, Vickers left the team at the end of last season to join the Red Bull Toyota effort. Casey Mears replaced him at the wheel of the #25. He has struggled this year, but hung on to win the Coke 600 last week.
Hendrick #25 Wins:
Richmond - 9
Parsons - 0
Hendrick - 0
Schrader - 4
Craven - 0 (did win 1997 Winston Open)
Sprague - 0
Bodine - 0
LaJoie - 0
Dallenbach - 0
Nadeau - 1
Nemechek - 1
Vickers - 1
Mears - 1 (so far)