42 until I gave up. I love Boggle.

(SPOILER)fat
fats
far
fart
farts
face
fate
fates
ash
rat
rats
rate
rates
set
star
sac
tear
ace
race
tee
tees
see
sheet
has
art
arts
oaf
tar
tars
say
fast
rash
cash
hart
harts
fact
facts
haste
trace
stray
stay
tao

EDIT: No, Shlup, the proper nouns don't count. Also, wow, I missed some easy ones. I should try playing when I'm not exhausted from playing basketball.