Prepare for a wall of text
I've got to admit that I'm not a fan of 'classic' punk, like The Sex Pistols, The Damned, The Ramones etc. As I mentioned before, my love of punk started with the Tony Hawk games and a few other video game soundtracks (Crazy Taxi was another). I ended up buying an Offspring album (Americana and it was my first ever CD purchase) and played it so much that my brother snapped it in half
I later got into Green Day and then kinda discovered all the East Bay skate punk bands that made it big in the late 80's/early 90's (Green Day, Rancid, Operation Ivy, Bad Religion, Pennywise etc). After fully immersing myself in those bands I discovered ska punk and especially some of the great UK ska punk/skacore bands that were about in the early 00's (Capdown, King Prawn, {Spunge} etc). From there I just discovered a mix of all different sub genres of punk. The following list is of all the bands I REALLY love:
AFI
Against Me!
Alkaline Trio
All
Allister
Anti-flag
Assorted Jellybeans
Authority Zero
Bad Brains
Bad Religion
Big D and the Kids Table
Bigwig
Blink-182
The Bouncing Souls
Bowling for Soup
Boxcar Racer
Capdown
The Casualties
Catch 22
Choking Victim
Clay Pigeon
Dead Kennedys
Descendents
The Distillers
Dropkick Murphys
The Dwarves
The Flatliners
Flogging Molly
Frenzal Rhomb
GBH
Goldfinger
Good Riddance
Green Day
H2O
Hard Skin
Hi-Standard
Jaya the Cat
The King Blues
King Prawn
Lagwagon
Larry and his Flask
Lars Frederiksen and the Bastards
Leftover Crack
Less than Jake
The Living End
The Loved Ones
The Mad Caddies
Masked Intruder
Me First and the Gimme Gimmes
The Mighty Mighty Bosstones
Millencolin
The Misfits
Morning Glory
Mustard Plug
New Found Glory
No Use for a Name
NOFX
The Offspring
Operation Ivy
Pennywise
Propaghandi
Rancid
Random Hand
Reel Big Fish
Refused
Rise Against
Rudebones
RX Bandits
Screeching Weasel
Sick of it All
Ska-P
The Skints
The Slackers
Social Distortion
{Spunge}
Star Fucking Hipsters
Street Dogs
Streetlight Manifesto
Strung Out
Sublime
Suicide Bid
The Suicide Machines
Sum 41
Swingin' Utters
Tiger Army
Tokyo Ska Paradise Orchestra
Tony Sly
Transplants
Uncle Brian
The Vandals
Vic Ruggiero
Voodoo Glow Skulls
Wizo
Yellowcard
Zebrahead
4ft Fingers
As a general rule nowadays anything that is released on Fat Mike's (NOFX) record label, Fat Wreck Chords, is worth a look. So many good punk bands signed to them.