"Cautious optimism" is the key here. The best case scenario, as many members have pointed out, is that Amazon only takes advantage of Goodreads' vast data store and doesn't interfere with the actual community behind this information. There might be an increase in certain types of advertisements, and more syncing with Amazon owned products or Amazon affiliates (for example, in giveaways, in compatibility with Kindles, in ads, etc.), but this best case scenario assumes that the basic functionality of Goodreads won't change.
The worst case scenario is that Amazon's policy of "your reviews belong to us" (which I didn't really realize until now, and am suddenly thoroughly uncomfortable by just how much I've given them over the years) will extend to Goodreads. That the functionality will go from a bookish social networking site that aims to build a community to another extension of Amazon's dominance in the book industry. That Goodreads' recommendation algorithm will be replaced by Amazon's significantly more commercial one. That the ease of finding old, indie or little-known books will evaporate. That the option of buying a book through an independent provider will disappear. The worst case scenario? Goodreads loses everything that made it the site that it is.
Personally, I believe in the middle ground. Obviously Amazon will be mining our personal collections now in order to better understand its customers, but is that necessarily a bad thing? I've complained for years about Amazon's stupidity when it comes to book recommendations, and the clumsy way it tries to throw the bestseller-of-the-moment at readers. With this new (and significantly improved) pile of data behind it, maybe Amazon will actually improve. Maybe it'll adopt Goodreads' book recommendation algorithm, and not the other way around. Maybe it will learn.
Goodreads is probably going to change. It's going to feel different, if only because everyone will expect it to change, and be on alert for any suspicious behavior on Amazon's part. Like most Goodreads users, I'm uncomfortable and nervous and a little upset by how brazenly Amazon has been going about creating a true monopoly in the book world. But I'm not about to delete my Goodreads account. Unlike most readers, I don't really need Goodreads to catalog my books (I have a significantly better Excel document that has much more information than I'll ever give the site...). I don't even use it for the social/community aspect very well, though recently I've made a bit more of an effort. I don't really like reviewing on Goodreads, and I don't necessarily love their recommendations algorithm. But all together, it's a convenient site. The ability to access simpler, more sincere reviews than Amazon is pleasant. Seeing the different methods by which people tag and label their books is fascinating. It's less severe than LibraryThing (which I also don't like because of its price tag), and it's less commercial than Amazon. Goodreads filled a certain niche in the literary world. Hopefully this will not change, even if other details do.