I'm not going to draw a hard and fast line between "old" and "new" Weezer. I think in my mind, probably Red and everything after is "New," but I think some die hards would start at Green.
Anyway, I've been doing some thinking, and I've decided I've been pretty hard on Rivers and Weezer. Pinkerton means a lot to me, and I'll admit to judging other Weezer albums against it. That's not fair, though; other albums weren't meant to be what Pinkerton was.
So, I've been trying to keep an open mind. I have a few break out favorites (remember, no hard and fast "New Weezer"):
Unspoken--This song redeems Hurley for me. He did this one acoustic on youtube and the Guitar Center Sessions, but I like the album version, with the build up and eventual entry of the full band, and the repeating of the chorus over and over. The lyrics aren't as complex as Pinkerton, but Rivers does well with simple lyrics and repetition in this instance.
If I had one critique, it would be that I'd have like to have heard electric guitars for the fills instead of woodwinds and what I think are violins. That's more of a personal preference, though. When I fell in love with Weezer at 16, before I even really paid attention to lyrics, it was the guitars that hooked me, and Rivers is So Good at what he does with an electric guitar. Is it true that this was about his wife? I can't remember where I heard that. I know I've felt like this in long term relationships before, and was glad to find this song.
Where's My Sex? I think this song is clever, and a lot of fun. I like when the guitars sound like the washing machine running. I'm not so crazy about the bridge, but this is a great pop song--suggestive, singable, and simple, but not brainless. A guilty pleasure.
Perfect Situation--semi-new Weezer. I included it because it's one of my favorite Weezer songs, and Make Believe gets a bad rap sometimes. Like I said, I like guitar solos, and these two are fantastic, and moving. Another example of Rivers' simple lyrics at their best. He manages to avoid "cheesy" and is still pretty confessional and revealing, which is what I love about him. The music video is priceless, too.
There are a lot of others, but this is getting too long. His newer songs aren't all perfect, but a lot of them have pretty good potential. I wonder if the pace at which he was releasing the albums has anything to do with the unfinished/unpolished feel of some of the songs.
Miss Sweeney is easily the best "new" Weezer song and is probably the closest thing we've gotten to the playfulness of the Blue Album and the heartfelt Pinkerton. This should have been included on the regular album.
The Underdogs is another gem in the last 3 albums which, again, is only on the deluxe edition on Raditude. I think it's universally accepted that Raditude is their weakest album, but The Underdogs is a great song in my opinion. It's catchy and seems pretty heartfelt. Another one that should've been included on the main album.
Ruling Me is my favorite song from Hurley, and evokes feelings from listening to old Weezer/ It's a fast, catchy song, and when Hurley first came out I couldn't stop listening to it.
Some older songs...
The Damage in Your Heart is a fantastic song. Make Believe is easily my favorite "new" Weezer album (in this case anything after Pinkerton) and this is my favorite song from it. It's got a great message, is heartfelt, and is overall just plain catchy. To those of you who hate on Make Believe, you should re-listen to it. It's really got a lot of great stuff in it.
Anything from Green Album all sounds the same, but I recently started liking it much more than I used to. For years the Green Album was, by far, my least favorite album. After disliking it for so many years, I just stopped listening to it and barely even acknowledged my ownership of it. About 2 years ago I re-listened to it. And you know what? It's actually pretty decent. My biggest with it was, and still is, the fact that almost every song sounds the same. But overall its a pretty decent listen. And yes technically this album is no longer "new" as it's been out for 12 or 13 years but I'm counting new as anything after Pinkerton.
I feel that most material from the Red era is really excellent. It was produced and mixed well, it was written well, it had interesting dynamics in the songs and unique and fresh feels. Greatest Man, Sweeney, Dreamin, Pork and Beans ,etc. I've even come to appreciate Everybody Get Dangerous more over time. It has great drumming, a nice drum solo outro. I really enjoy that era of Weezer. Songwriting was pretty good during Make Believe and Green too, but they really were onto something with Red.
So I guess what I'm trying to say in a long-winded roundabout way is, I really liked the Red era most haha. It's too hard to pick a single song (or even set of songs)
"Pork and Beans" is clever and still one of my ten favorite Weezer tunes. "Can't Stop Partying" is catchy and on another level serious. The Green album is still my favorite album and if done on tour I'll be there.
Like many of you have said, new is a relative term. I like stuff that most fans consider solidly new like "The Greatest Man That Ever Lived", "Trampoline", "Trainwrecks", and "Ruling Me". Rivers IS a genius. A sign of genius is becoming bored easily. That's why the most creative artists like to try lots of different things. Someone asked Kirk Hammett once how to become a great musician, he sid something that I have remembered ever since: LISTEN TO ALL DIFFERENT KINDS OF MUSIC.