Your count += 1
indentation is wrong.
CORRECTED:
MODE = ["Only Even", "Only Odds", "All Numbers"]
for i,v in enumerate(MODE):
print i+1, v
count = 1 #changed 0 to 1
s = int(raw_input("Enter Mode Wanted: "))
if s == 3:
while count <= 10: #changed < to <=
print count #changed count+1 to count
count += 1
elif s == 2:
while count <=10:
if count%2 != 0:
print count
count += 1
elif s == 1:
while count <= 10:
if count%2 == 0:
print count
count += 1