Was experiencing something like this on an early 2011 Macbook Pro running OS X 10.8.5. Several minutes *after* startup the machine and screen would freeze, and would begin beeping three times (while the sleep light flashed in unison) every five seconds or so. This is slightly different than the un-seated RAM issues described elsewhere, which seem to happen at startup and result in a gray / green busted screen, but was also quite worrisome: it appeared that I had RAM that randomly became unreliable--or perhaps an even more dire hardware problem.
I found a thread on a Google Drive product forum that seemed similar, albeit for 10.6.8. Google engineers ultimately confirmed that the problem was repeatable, and as a result of Google drive. The thread was (unhelpfully) closed (I started a new one here). The best explanation of this came from @tallted, a user who reported replacing his RAM before taking the machine into the Apple genius bar. "the Apple Genius dove deeper into the Console logs. Apparently, the three-beep klaxon alarm happens anytime the machine can't *write* to RAM, which can be due to software *as well as* hardware failure."
This would seem to contradict Apple's official current guidance here, which, as of today, doesn't mention the possibility of a software problem. It just says that: "3 successive tones, a 5 second pause (repeating): This indicates RAM does not pass a data integrity check." Reports elsewhere on the internet suggest this has happened when installing parallels as well, presumably a software issue there as well.
That said, @tallted's genius' explanation does seem consistent, in a way; if google drive has (buggily) remapped the way data is written, perhaps an error in writing to their storage would look like an error to write to RAM.
What was especially nebulous about this problem was that there was no obvious link to google drive--my computer just froze and started beeping several minutes after startup. And yet erasing the google drive app seems to have resolved it.
System is similar to Ricarado above:
10.8.5
15-inch early 2011
Processor: 2 Ghz Intel Core i7
Memory: 4 GB 1333 MHz DDR3
