I think everytime this comes up most people--including on this site--try to take far too logical approach to it. How dominant is x-program. In my mind that's not what a helmet program really is. A helmet program is one that gets a huge amount of respect, publicity, and attention not because of how dominant it is right now, but because of...wait for it...the HELMET they wear. Now, this is impacted by the program's dominance, but it's more its historical and cultural dominance, than it is the actual wins and losses.
So Alabama is a helmet school because (1) it has an easily recogonizable helmet, the basics of which will not change because that crimson helmet with a single white stripe and the nubers is a brand identity that Alabama fans would lose their minds over if someone suggested changing it; and (2) Alabama built that brand identity through decades of impressive football results. That's really what this is about: brand identity as expressed through helmets.
Other helmet teams: Notre Dame (sure, they change the shade of gold, but the helmet retains its brand identity, regardless of the shade); Ohio State--grey, red, and buckeye stickers; Michigan (stolen from Princeton or something?), Oklahoma, Univ. of Southern California, Penn State. These are teams that have recognizable brand identity, based on their helmet design (notwithstanding tweaks they may make), and an association with historic wins.
Others: Nebraska. Notwithstanding the last decade, people still recognize that plain N on a white background with a red stripe, and they think: college football royalty. On hard times? Sure, but still part of the brand. Texas. People just want to believe Texas is great. Florida State and Miami. I think because they were so strong as TV rights and CFB were coming of age. Actual helmets with brand identity that is associated with college football dominance, even if it isn't especially current.
I think those are the true helmets. Do others deserve to be discussed? Probably.
In the conversation: LSU, Tennessee, Florida, aTm (even the way I write that suggets the strong helmet brand identity), UCLA, Washington. Lingering around: Oregon, Wisconsin, Auburn, maybe Tennessee (surely it included Tennessee a while ago, but that brand has waned a little)...
I'm sure there are others, but that's my hot take.