They were good at the iTunes Store, which is an Internet service wrapped in software. However, I have never quite understood how the iTunes Store has stood the test of time . . . I guess it's kind of like AOL and gets ingrained in people's patterns. It is easy to use and it's there when people are syncing their devices, but I would say they have made the interface worse (I can't remember when they switched to the current web-page like interface, but I don't care for it, scrolling horizontally and vertically on the same page is difficult). iTunes as software has become a monstrosity serving system wide functions, and I would say the program is less intuitive than when it was introduced.
Going way back, they also kind of failed at eWorld; although, I will say eWorld had attractive icons!
MobileMe is very useful, but as someone who had to attach it to orders (worked at Apple as a contractor in sales), I will say it was very hard to sell. It was extremely difficult to say in one sentence what MobileMe does, which is one of its problems. AppleCare was very easy to sell in comparison. MobileMe has quite a bit of downtime for me, too. And just trying to click on iDisk still to this day will sometimes bring the Finder to a crashing halt.
Ping was just sort of like an idea thought up by marketing people. I have no idea what its purpose is. I have written before how I thought they could have made it better, but I won't rehash all that.
I would say that Apple seems much more comfortable writing software where they control all the pieces. MobileMe on the web even has an application-like feel, but it's not as reliable or usable as other services. It feels a bit like using something that is pretty, but I don't even really trust it, especially sending mail from MobileMe on the web. It just doesn't feel "real." Not to mention that when MobileMe first came out, you couldn't even access it from IE 6, which is one of the browsers you're likely to encounter in the wild when away from your computer (esp at that time, but still in many rural parts of the world). Galleries on MobileMe are also very hobbled. You can't link directly to photos, can't view pics in very large sizes. Can't add files to iDisk and have them show up online in a public directory. Apple sometimes designs things to the point that if you wanted to do something other than what they predicted you wanted to do, you're stuck. They used to be the opposite when they first came out with the Mac. They came up with a very clever, simple paradigm of how things worked, and you figured out how to do things using simple, consistent rules. I would say Apple has become more Windows-like in that a lot of its programs including iLife are almost like Windows Wizards that take you through tasks that have an end result in mind, such as making a movie trailer, photo book, etc. They expect you to export to their services, rather than allowing you to drop a photograph onto your iDisk a la FTP and have it show up on your server space. I know you can also export to other services, so that point doesn't stand entirely. What does stand is that they make somewhat closed systems, and somewhat less intuitively than the past. I think to make a great social Internet service you would need it to be both of those things: intuitive and allow for user invention. I don't think the founders of Facebook had any idea what it would be used for, or the founders of Twitter for that mater. It's about building a platform where you, the user, can use the rules set up to accomplish something, rather than what the system predicts and wants you to do, just like on the original Mac. Ping, for example, just wants you to share that you like music on iTunes. That's not open or inventive. You might as well just put the Apple sticker on the back of your car to say you like Apple, that's all Ping really accomplishes, promotion of iTunes Store by its own users, and who wants to do that?
But to answer your question. I don't know if they can make a great service. I would imagine there is a lot of pressure on not allowing iCloud to fail like MobileMe did a few years ago. Want to know something funny? I'm gonna back up all my e-mail and stuff from iDisk before Monday just in case. That's how much faith I have in their Internet services.