I like AC/DC alot for its rules, your working your way through the jukebox but you can do it in any order you like. There is a lot of strategy of what song to play at what point and when to cash in the jackpots. Very deep rule set. The Walking Dead seems to be very popular for its rules these days, it's kinda had a resurgence. JJP games are pretty mode based. There are so many its hard to list, lots of classic like The Adams Family, Jurassic Park, The Shadow.

Lots of games fit your criteria. Most mode based games are non-linear.

TWD
LOTR
ACDC Pro (prem has unbalanced scoring via Hells Bells)
Shadow

Those are my favourites, their modes/scoring balance is why I have them.

In LOTR you don't have to complete the modes, but there are valuable rewards (gifts of the elves) for completing them which are required to progress to wizard mode. Unlike TSPP, you cannot stack modes.

Unfortunately most games have modes that time out... I didn't realize that you were looking for games which require you to complete the modes. That usually applies to more linear games, like GB. Star Wars might 'force' you to complete modes, but I don't know the game well enough to say with certainty. Perhaps you are a fan of the Dwight Sullivan rule styles. (He did GOT, GB and SW)

GOT rules are definitely great.

Most games allow you to select the specific mode that you want to play and don't require modes to be played in a linear fashion. Sometimes it isn't obvious how to select a specific mode, but usually you do have the choice in the order that you play the modes.

All 4 of the games that I suggested allow you to choose the mode that you want to play in any order:

TWD - Choose mode by shooting specific shot
LOTR - Flipper buttons change lit mode
ACDC - Choose any mode once in jukebox
Shadow - Change lit mode using ramp shots

I enjoy the Mustang modes and the ability to choose what one to start and which one to play next when completing a mode. Also help to change up the songs to ones you enjoy - great mode based jukebox on Mustang.

I also began to tire of Metallica and sold it. I prefer more traditional mode based games I guess.

It's hard to think of any Mode based games that are linear besides PM & GB. Most are not linear.

Road Show always comes to mind

Also, FYI, tiltforums.com is a great place to discuss the finer details of actually playing pinball.

Pinside is more of a general pinball talk/news/marketplace forum. Not saying that this doesn't belong here, but you'll get more thoughtful responses re: playing pinball over there.

SW is definitely in the same vein as GoT. The only game I can think of where you can't time out modes at all for better or worse.

Metallica is fun and a blast to play, I love the band, and the theme is very well integrated. But, it got old for me cause it became quite repetitive. But it's a great pin to revisit from time to time due to its depth and fun. But after one or two plays I feel I've gotten all I need from it for awhile. That said, GOT to me has one of the best rulesets in pinball. It synergizes so well with its layout and has so many unique things going on. If you're looking for a pin similar to it, give Star Wars a try - it's GOT on steroids. Though I do prefer the layout, theme, and sound of GOT - but Steve Ritchie and Dwight Sullivan took that type of ruleset to another level with Star Wars. Adding all sorts of little mini achievable wizard modes that can be accessed different ways from game to game.

Some other pins that offer this type of depth and breadth would be TWD and WOZ. TWD has so many wizard modes to achieve and its new code fixes the funnel hole that made horde the center of attention. WOZ is awesome with so many unique paths and each area of the pin has its own end mini wizard mode.

I am very curious to see how JJPOTC ends up being as this is the direction they are taking, I just hope it doesn't back fire on them by putting in too much making it a marathon style game needed to advance or open the game up. There needs to be balance amongst all available wizard modes; and making those attainable wizard modes different each time they are played is key. Dwight nailed this method of madness rulesets with GOT & SW. A fine balance of depth and breadth is a recipe for a fine home use pin. Some games get so wrapped up in having so many modes that the ruleset becomes overload, and ultimately ends up being more work than fun.

Linear or Non Linear?

Judge Dredd has nine non linear modes that lead up to one major non linear mode.

How about America’s Most Haunted. If you’re looking for something cheaper, JP Lost World requires you to complete modes and it’s a tough game

Do all the modes in AMH have some second phase (MB?) ? None around here so I'm not too clear on the rules

Yeah I believe a couple end in a multiball. I like the game because it has tasks to reach the wizard, which is one of the toughest out there to get to. And you have to complete the modes or you do not get credit. One mode even gives you a ball save if you drain during the mode

#star_trek is non-linear for the most part. You can choose any of six modes to begin with and after completing one you can either play a different one or another level (more difficult) of the same one. I think the wizard modes are linear, I don't think it's possible to play five year mission before kobyashi maru.