Rarest would be Infamous 2 (3.5%), Playstation AllStar Battle Royale(2.3%), Infamous 1(1.9%) and Unit 13(1.3%)
Most common plats would be jak and daxter:the precursor legacy(17.2%),(Virtues last Reward (23.9%) and the walking dead(39.4%)

My rarest seems to be from Tales of Graces, and most common looks like the Walking Dead...

I don't have many plats...

My rarest is Hyperdimension Neptunia with 13.15%

My most common one is Sly Cooper band of thieves at 60.97%

My most rarest trophy in general is LBP Create The levels you have published were hearted by 50 or more people and you were hearted by 30 or more people at 5.64%

0.9% in DCUO for PS4. Easy trophy, really, just have to level six characters and spend at least five dollars on the game. It also unlocks the PS3 version's trophy.

Most common Platinum? 36.4% on inFAMOUS: Second Son.

Edit: Wow, I was off. Psntrophies.com does not have very accurate percentages. 

My Rarest is actually DCUO for PS4 at a whopping 0.1%, and my most common is inFAMOUS: Second Son at 7.9%

inFAMOUS 2 pulls up with 21%.

Edit: My bad, I am incorrect. 

Rarest is Velocity 2x at .2%. (Super Time Force and New & Tasty were runners up at .3% each.)
Most common is Walking Dead Season One at 46%.

Edit: Well, just got the plat for Gauntlet. .1%. The grind was real. Whoever thought killing 15000 orcs was reasonable should be smacked.

Rarest: Assassin's Creed IV Black Flag PS3
Most common: Walking Dead season 1 PS3

I only have two: The Order 1886 and Grim Fandango. Last time I checked Grim Fandango, the Plat was at 4% or so, so that's my rarest, while The Order was at 6.5%, so that's the most common one I have so far.

My rarest and only Ultra Rare platinum is Grand Theft Auto V (2.33%), followed by some Very Rare ones like WWE Smackdown vs Raw 2011 (5.56%) and WWE '12 (6.48%). But I'm much more proud of Metal Gear Solid Peace Walker (7.79%). I'm thinking on getting GTA V's platinum on PS4.

The most common (and easiest) of my platinums is Infamous: Second Son (36.04%).

i have respect @ all guys, they have platinum trophie by a "Yakuza"-Game :)