It's pretty hard to go wrong selecting ten “best” or ten “favorites” from the Criterion Collection, although it might be interesting to select the ten worst Criterion releases (something that, in deference to my friends at Criterion, I will not do). As a longtime cinephille I'm familiar with most of the Criterion catalogue. Rather than select ten favorites I'll choose ten films that I was able to see because of Criterion, films I previously did not know about or were not available.
Biography via Criterion.

Víctor Erice
1973
98 min

Larisa Shepitko
1966
100 min

Juan Antonio Bardem
1955
88 min

Hiroshi Teshigahara
1966
122 min

Anthony Mann
1950
109 min

Mikio Naruse
1960
111 min

Gus Van Sant
1985
75 min

Rainer Werner Fassbinder
1980
60 min

Francesco Rosi
1963
101 min

Kenji Mizoguchi
1956
87 min