Which counties have never won the sam maguire cup?

The total answer is 16 counties. Firstly, 13 counties have never won the All-Ireland Senior football title:

1. Antrim
2. Monaghan
3. Fermanagh
4. Sligo
5. Leitrim
6. Waterford
7. Clare
8. Kilkenny
9. Wicklow
10. Westmeath
11. Carlow
12. Laois
13. Longford

The Sam Maguire Cup was first awarded in 1928, so counties that won the All-Ireland Football title before that, but not since would also have never won the Sam Maguire Cup. Those counties are:

Limerick, Wexford and Tipperary.