How many trophies did Nottingham Forest win under Brian Clough?

Thirteen as follows:
2 x European Cup
1 x UEFA Super Cup
1 x Intercontinental Cup
1 x League Championship
4 x League Cup
1 x FA Charity Shield
2 x Full members Cup (at the time known as the Simod Cup)
1x Anglo-Scottish Cup (which Clough attributes as the one that started their winning habit)
The Football League Centenary Trophy ( a one-off tournament to celebrate 100 years the the Football League)

They also went 42 league matches without defeat over exactly 1 year, from 26 November 1977 to 25 November 1978. A record which stood for 26 years.