IBM did successfully enter and even define the PC market.
Microsoft saw the threat of the Internet, and reacted swiftly to own it with Windows 95. Internet Explorer demolished Netscape, with illegal methods, but most people at the time also recognized IE as the better browser. Microsoft also got a strong foothold on mobile with WinCE/PocketPC/Windows Mobile.
Google was an early entrance in social with Orkut, dominating some important emerging markets (Brazil, India).
In each case the companies seemed to lose interest and refocus on their moneymaker divisions. It might be intrinsic to large companies: If you want to advance, you should work where the money is made. So the best and most ambitious people would go there, leaving the forward looking parts of the company to die of negligence.
No they didn't. The original release of Windows 95 didn't come with Internet Explorer. Microsoft were still trying to push their own Microsoft Network (MSN), similar to Compuserve and AOL. They were late to the party - which is why Netscape managed to dominate for so long - and were heavily criticised for it at the time.
Thankfully, they failed. Even though IE dominated the web for far too long, that's a lot less scary than the thought that everyone might be using the MS Network right now while the Internet remained an academic curiosity! shudder
There are cases to be made for these reigns being useful: AT&T spawned Unix and (in part) TCP/IP and the Internet, IBM spawned much IC development, Microsoft proliferated cheap and standardized x86 CPUs. But each also quashed competition in the form of both other firms and competing technologies: AT&T, despite the role UNIX came to play in packet-switched networks, explicitly rejected them for its own network recognizing that this would undermine its own dedicated-circuit switching. Microsoft's treatment of competitors is legion, but it's IBM we have to thank for the term "FUD".
All of those ads prompting you to visit a company's Facebook page are today's version of the "find us at AOL keyword So-and-so" that you used to see all the time in the late 90s.
I'd count Yahoo as another dead contestant.
When dial-up was the only option to get "on-line", AOL was dominant. Those discs (and later CDs) were everywhere. The problem was, even though providing a dial-up connection is what made AOL into the behemoth it had become, I'd argue the real value proposition of AOL in the mid-to-late 90s was the "walled garden" version of the internet that they had created.
So, instead of bolstering their offerings in the "walled garden" arena, they fretted over the death-grip they had on their dial-up subscribers long, long after it became apparent than DSL/Cable had won the battle for your connection. (No seriously, they still have that death-grip...have you tried canceling a free AOL trial account recently?)
AOL "died", as most oversized companies do, by failing to pivot toward an emerging market in favor of holding on to their "sure thing". Look at your other examples: IBM failed to pivot away from mainframes (their sure thing) to PCs (the emerging market). Microsoft has failed to pivot from OS/Office software to Cloud/distributed computing. Apple, eventually, did manage to pivot from graphics and design to mobile devices. Google...well, Google pivots so frequently I'm surprised they don't collectively vomit from dizziness (though, they do still have a worrying dependence on search advertising for "real" revenue).
The reason I think AOL is probably the most apt example for Facebook to consider, though, is that Facebook was the primary beneficiary of AOL's failure to capitalize on the "walled garden" internet. Now, Facebook dominates this realm, but the question is for how long? You're idea that they should pivot towards photo sharing is interesting...but I couldn't say for sure (or, if I could I'm making waaay less money than I should be).