If I understand you correctly, I think you could do it as follows using pandas. I'll start with the series before you split the strings:
print s
0 one two
1 two seven six
2 three one five
3 seven five five eight
4 six four
5 three
stacked = pd.DataFrame(s.str.split().tolist()).stack()
print stacked
0 0 one
1 two
1 0 two
1 seven
2 six
2 0 three
1 one
2 five
3 0 seven
1 five
2 five
3 eight
4 0 six
1 four
5 0 three
Now just compute the value counts of the Series:
print stacked.value_counts()
five 3
one 2
three 2
six 2
two 2
seven 2
eight 1
four 1
dtype: int64