In 1981, Bill Gates said that "640 k ought to be enough for anyone"
Here's the background: For quite some time, a PC couldn't use more than 1 MB RAM, i.e. 1024 kB. Of these, 384 were reserved for the system, and 640 left for the user. In the early 80's, this was an awful lot of memory, not to mention that it cost an awful lot of money, so initially it was hardly considered as anything but a theoretical limit. This soon changed, however, and various work-arounds had to be developed. Now, this is thankfully history, but many of us have cursed that silliness over the years (have you ever experienced a game that won't run because it's a few kB short of memory, despite being run on a machine which has several megabytes left?), and wished they had went for a much higher limit when they had the chance. Like 16 MB. Or 64 MB, or... With 32 bits you can address 4 Gb directly, and who knows how long that will last?
This wasn't, of course, the first or last time such limits were set; all systems that handles memory, or does some other kind of addressing, have built-in limits somewhere, and when they are designed the limits are set comfortably high. But that doesn't mean the designer is convinced that the limit will suffice forever. (A similar example in the Macintosh world is the inital limit of 128 fonts - not on a single machine, but on all Macs, worldwide. This fact is somewhat less well known than the 640 kB-quote.)
That's how Bill Gates reason when he denies the quote:
I've said some stupid things and some wrong things, but not that. No one involved in computers would ever say that a certain amount of memory is enough [...] But even 32 bits of address space won't prove adequate as times goes on [...] Meanwhile, I keep bumping into that silly quotation attributed to me that says 640 k of memory is enough.
The supposed quote resembles an excuse, and many believe that the limit was set by Microsoft, but it wasn't; it was an hardware issue, the main reason being that the 8088/8086 architecture could address 1 MB of memory. If you ran DR-DOS, or any other non-Microsoft OS on a PC, the limit was still there. Some argue that if those 384 kB of reserved memory had not been in the top of that megabyte, it would have been easier to work around; anyway, if you want to blame anyone, blame IBM, because they designed the hardware.
Only when Intel launched the 80386, which could work with 32 bit addresses, the problem was finally solved - at least for a while...
To sum it up: Though many believe, and want to believe, that Bill Gates said such a short-sighted or downright stupid thing, I consider it a myth, until proved otherwise - and it's noteworthy that no one has yet shown exactly when or in what context he said it, only that it was in 1981, the year the IBM PC was released.