I'm 25 and became a fan about 4 years ago thanks to my uncle.
I consider myself a fairly level headed guy when it comes to being a fan of something (limiting expectations, not buying masses of merch etc), but Twin Peaks really does push all my buttons and is without a doubt the thing I love most in the whole world just behind Pizza and my GF.
I think it genuinely does hold up amazingly well. It's all down to it's style. There really is nothing else quite like Twin Peaks. It's part sitcom, part soap opera, part full on drama and most importantly part psycho thriller. There's just so many facets of novelty and intrigue to it. It simultaneously feels so of it's time yet completely timeless. It's much like Lynch's films. That sense of surreal consternation yet complete sense of intrigue is part of what makes his work SO enduring.
However, like everything, it's not perfect. There's a reason the show was discontinued during the second season. It get's very slow once the central mystery is all but wrapped up and it's clear that Lynch and Frost lost all sense of direction from then on. However, it's worth watching until the very end because the cliff hanger is fantastically brutal and dark. 'Fire Walk With Me', whilst not as good as many of the best episodes, I maintain is still a great movie that helps round off some of the characters and plot points fans felt where a little under served.