Music

Mighty Mighty Bosstones and Reel Big Fish are both classics. Im also a big fan of Madness. For Ska-Punk you cant beat Less Than Jake

Straight up ska (in addition to what other people have said): Streetlight Manifesto, Mad Caddies, The Interupters, Big D and the Kids Table, The Specials.

If you wanna go old school and to a couple of biggest influences on modern ska and way more punk: Choking Victim (later morphed into Leftover Crack) and Operation Ivy (morphed into Rancid).

Roots (like ska but a bit more chill): Stick Figure, The Expendables, Rebelution, Pacific Dub.

You may also like Sublime and the band made after that Sublime with Rome (although personally I don't).

Also something not quite ska but kinda in the vein of, shameless plug for a great New Zealand band called Fly My Pretties.

Suburban Legends

Me First and The Gimme Gimmes do amazing ska covers of popular music.

Thanks all. I'll check out all of these. I'm a big Less than Jake fan.

https://whatdoyouknowaboutskapunk.bandcamp.com/album/what-do-you-know-about-ska-punk-vol-1

Despite being a Christian/religious group, Five Iron Frenzy are great.

The Night Gaunts get slept on a lot. Also great are Streetlight Manifesto, The Suicide Machines, Arrogant Sons of Bitches, Bomb The Music Industry!, Mad Caddies, Simple Minded Symphony, and Faintest Idea.

Magadog!

Tokyo Ska Paradise Orchestra, if you haven't heard. https://www.youtube.com/watch?v=RvHTLhz02vo

Kill Lincoln are really good

The Toasters

I always liked the Mr. Twist album by Let's Go Bowling. The Skeletones and Skatelites are fun too.

Ska-P, obviously

There's so many sun genres but I always liked "crack rock-steady" which is more hardcore punk/metal influences. Leftover crack has already been mentioned but No Cash is another good one in that vein. All that's no horns though.

You mentioned you like Less than Jake so I'm guessing you like the horns and the more bombastic sounds compared to the reggae bass sounds. Only bands like that off the top of my head are Voodoo Glow Skulls. Idk if you can find them anywhere but Link 80 is awesome too. They're just good, straight up skate punk with some great horns. Old "give them the boot" and "Asian man records" complications would have a lot of different stuff too.

"Ska sucks" by Propaghandi is a must listen song too lol