There are 16 Trophies that can be collected.

Bronze

Time is Money
Give a top answer in the first 5 seconds 10 times

Points Vessel
Earn 1000 points in Fast Money

The Beginner
Win your first match

The Magnate
Earn $500,000

The Comeback
Win 5 Sudden Death match

The Thief
Steal the board 10 times and give a good answer

Survey Beast
20 top answers during Faceoff

Counteroffensive
You get behind for primal 3 rounds but exceed at the last round

The Loser
Get the 100th strike

Unlucky Baby
Be stolen by other families for 10 times

Win Win
Two families get exactly the same points at the 4th round

Taste of Winning
Beat 10 rivals online

Silver

Super Board Cleaner
Complete the board 20 times without a strike

Hollywood Champion
Go through the game under any difficulty

You Are Historian
Win all ages awards

Dare you challenge me
Beat 30 rivals online

http://www.ps3trophies.com/forums/playstation-trophy-news/8104-family-feud-decades-trophy-list.html