I've been a listener for a long time, and their recent "Premium" option caught my eye. $36 seems pretty reasonable for better quality, a desktop player, and the ability to listen without screwing with the client for 5 hours. Makes running around in Champions Online a lot more lively when you're blasting a Gorillaz station. I only wish it included the mobile option for us non-smartphone AT&T owners, so I wouldn't have to pay $10 a month to listen through my phone. For that price, not happening.

last.fm

I used to love Pandora.
They've been bogging it down in too many restricting skip-related rules and advertisements lately, that I'm having trouble listening to it. Plus, all the bands I like...it only seems to play 3 songs over and over. Boo.

I'm a clunky old fogey and just listen to MP3s

The ad-skipping works well for the premium edition, but it stinks that it only plays 3 songs for your bands, and the premium edition still limits you to six skips per hour. I guess that's licensing for you.

ditto this, I like not having my listening experience broken by buffering

Same here... Along with the buffering there is regional restrictions, internet caps, advertisements... It's far easier and better to load up several tens'o'gigs with better control.

I used to Pandora before the restrictions for free in HK (around 2005, 2006 I think), then I was shut out of the US-only thing. So it's Last.fm, and I'm not going back.

I have the desktop client, is there something besides the Adobe Air one? To my knowledge, it's the exact website inside a window that minimizes to the status bar instead of the task bar.

All I know of is the Adobe Air one, which I have. However, there's some Mini Player option on the site, which I think does what you're talking about.

If your only goal is to get a desktop player, look into OpenPandora. Even lets you scribble for last.fm.
And I also prefer mp3s (if only, because sometimes I just want to listen to five or six covers of "Enjoy the Silence" on an endless loop), but nothing is better for finding NEW music than Pandora and Last.FM.
That being said, I prefer Pandora for finding radically new stuff, whereas I prefer Last.FM for listening to when I am at work or busy restructuring my mp3 library. Last.FM tends to actually give you stuff along the lines of what you seed the station with, whereas Pandora tends to be a lot more hit and miss, but also leads to revelations such as "Wow, I actually really love Christian Metal. Who would have thunk it?"

Nah, that was just the radio feature, and their excuse was licensing, but those in US, UK, and Germany will still be able to listen to it for free, and others from other locales can simply pay. The problem with Pandora is that they won't even take your money if you live anywhere BUT the US, which is so stupid.

For a little while I was using Pandora to find some new music, but although it did give me some good starting points, for the most part it just lurched wildly from one detestable extreme to the other.
"Oh, you don't like Cannibal Corpse? Here, try The Stone Coyotes."

It's really fail when it comes to that. When I used to use Pandora a few years back, I remember saying I liked U2 and instead of being given more "alternative rock", I was slapped with a horrendous amount of The Clash, and when I said I didn't like this punk shit, I ended up with... Yanni? Weird.
Whenever people ask me about Pandora, I usually just link them to this Wired article about Pandora I find interesting, which I'm doing now.