The worst production and mixing I've ever heard is on the CD version of Pink Floyd's Piper At The Gates Of Dawn. It absolutely hilarious. Listen to it on headphones. Most of the songs - 'Lucifer Sam' and 'Matilda Mother' come to mind - have pretty much no left side for about half of their length.
I hate the production on Time Out Of Mind by Bob Dylan, and most of Daniel Lanois' work in general. Dylan's songs are fantastic on that record, and 'Love Sick' is one of his best tunes. It's sparse and murky, and it works. But the novelty of an effect on his voice wears off VERY fast and it smothers the songs.
As for my favourite productions, I have a few. Whilst a lot of the rapping on it is actually pretty bad, Dr. Dre's 2001 album has some of the finest production I've heard on a rap record. It's slick, it's shiny, it's textured and detailed but not cluttered. Fabulous stuff. The strings and massive beat on 'The Next Episode' are absolutely great.
I love the production on Powder Burns by the Twilight Singers because it's absolutely kitchen sink, really lush and dark. It's kind of like Spector's Wall Of Sound. Everything is thrown in there, and yet it works. Similarly, the first BRMC record is great in this way because there are sheets and layers of everything all clamouring for your attention, and to a lesser extent Love Is Hell by Ryan Adams.
At the opposite end of the spectrum are the records I approve of because of the minimal or absent production. Nick Cave's Boatman's Call album, particularly 'Far From Me,' comes to mind because it's got more space on it than it has music. It lets the power of melody, the most impact from the few instruments, and the strength of Cave's songs really shine though. This also applies to Interpol's Turn On The Bright Lights. There are occasional echoes and reverb, but apart from that it's quite spacey, expansive, and mostly dry.
Some of my favourite productions are predominantly live, and this is mostly Dylan (but also applies to Jacksonville City Nights by Ryan Adams). Desire has him with a ridiculously overcluttered band, but they still recorded mostly live and I like the way it sounds. The massive screw-up in the middle of 'Hurricane' makes the record feel homely. Also his most recent one, Modern Times features a band occasionally augmented by lap-steel or strings, but mostly just the band and it still sounds very lush and warm.