So what's the Big Cat?
Really? You're going to open with that?
OK, fine. I'm guessing Cougar, but with all the iCloud business going on, I could see Clouded Leopard being a potential choice, although I'd be the first to regard it as kind of kitschy.
Potential Features of OS X 10.9 Cougar
The Demise of the Desktop
No, desktops will not be going away. As I've already said, they're going to get updates this year like always. What will happen is that, even more so than last year, the updates OS X will get are going to be tailored to the smaller-screen, power-efficient-over-brute-strength style of laptops over desktops.
Last year, full-screen apps took the UI of OS X whole hog, Mission Control and Launchpad took over for Spaces and Expose, and multitouch gestures augmented the UI. The one thing all of these things have in common is that they greatly enhance the useability of a laptop and are pretty cumbersome on a desktop, if they work at all and don't actually detract from the experience. Even features like Power Nap are geared toward the useability of laptops when they're closed - not one update was directed toward the desktop computer. (I'll let the multiple-monitor crowd talk about full screen apps, and share their pain and frustration with you in private.)
It's fair to say that this is a smart strategy for Apple, and it will continue this year, as it will most likely continue for the duration of the lifespan of the desktop computer. Expect features that fit that style - great on a laptop, useless on a desktop.
iCloud served its purpose in migrating settings from the iOS devices of millions of users to their brand new toys, but it's time for some of that stuff to flow downstream. iCloud should have a lot more data from system preferences and settings on the desktop than it does now, so multiple Macs stay in sync as far as preferences are concerned. (I also think there's going to be Preview for iOS to sync documents and PDFs back and forth everywhere, but that's for the next section.)
The main thing iCloud needs to do, though, is get better. Not just feature-better, but reliability better. That's why I wouldn't be surprised if iCloud doesnt add many new features, but they market an increased level of reliability.
New UI Paradigms
Everybody forgets that Jony Ive is not just the UI designer of iOS, but also as of 2012 the UI designer of OS X. Remember the book layout of Address Book, the "notes in a leather notepad" look for Notes, or the faux Corinthian leather lining of Calendar? Yeah, gone. From what's being said around their campus, the word of the day as far as Apple UI design is "flat".
Well, not exactly new apps. This might be wishful thinking, but I think this is the year iTunes gives up its control of the device ecosystem and lets iCloud shoulder some weight. I'd like to see App Store be the locus for all Apps, an iBooks for OS X that takes care of the iBookstore and a dedicated Podcasts app (I'd say this is why they pulled it out of the Music app on iOS). I could even see Quicktime become a more useful Media Center, or simply "Videos".
Also, Safari 7 will release with it, and I'd imagine it's a full Webkit2 browser with support for even more CSS3 and with greatly enhanced JS rendering. It'll leapfrog Chrome as the fastest browser on OS X...for two months.
What I'd Like to See
In order: a new file system, retinafied system fonts, updated features for the Finder (TABS TABS TABS), updated iWork apps, a replacement for the traffic-light (green is redundant with Full Screen), and the removal of legacy cruft like Stickies.app.
These are obviously blind foolish wishes, and all of my guesses are blind guesses, blinder than even my assumptions of Apple's hardware lineup. Software is where Apple still has retained the ability to truly surprise, and OS X and iOS remain areas where we know little to nothing about even what to expect, much less what we're going to see.