OK, here's my list!!
1. Super Smash Bros. (this was a really tough choice for me)
2. Final Fantasy
3. TimeSplitters
4. Street Fighter
5. Super Mario
6. Megami Tensei
7. Metal Gear
8. Silent Hill
9. Tekken
10. Crash Bandicoot
Honourable mention especially goes to the WWF/E franchise, not sure if it should be considered as one whole franchise or not though.