This video compiles all of Family Guy's unique intros, including parodies and spoofs. Not included are the Star Wars parodies and the intros from the "Road-to" Series. Those will be in separate videos. 

If you're looking for all the original intro variations, "mess-ups", and fails : https://youtu.be/1G19Z6yPs44

TIMESTAMP:
Law & Order: 0:10
The Naked Gun: 1:01
The A-Team: 1:57
Justice League/All-New Super Friends: 2:52
The Incredible Hulk: 3:50
Little House on the Prairie: 5:03
Monty Python: 6:19
Valentine's Day: 7:20
King of the Hill: 8:52
Modern Family: 9:25
"Follow the Money" : 9:40
"And Then There Were Fewer" : 10:28


Links to each Reference:
Law & Order: https://youtu.be/mrrCbjVqFBA
The Naked Gun: https://www.youtube.com/watch?v=0LIHoEJAA4k&t=183s
The A-Team: https://youtu.be/_MVonyVSQoM
Justice League/The All-New Super Friends Hour: https://youtu.be/RnxN-ZT9EGE
The Incredible Hulk: https://youtu.be/M7Hh063ZtsA
Little House on the Prairie: https://youtu.be/Vt4z16n-3eU
Monty Python: https://youtu.be/-rutX0I6NxU
Valentine's Day: https://youtu.be/1K45RdE2qlk
King of the Hill: https://youtu.be/LUZIQufgukA
Modern Family: https://youtu.be/h66TdMI5n5I
"Follow the Money" : N/A
"And Then There Were Fewer" : N/A