Let me give a few examples:
Google uses #609, #15C, #12C, #093 ...
Adobe uses #ECECEC, #D9D9D9, #B0B0B0, #737373 ...
Yahoo uses #f9fafa, #93B9D9, #fefefe ...
If you look at the CSS of most of such sites, the hex color codes they use are extremely easy to remember, and I don't think it's unintentional at all.
In case I am not clear as to what I exactly mean by "easy-to-type" hex color codes, I meant color codes like these -- #FFFFFF (#FFF), #15C (#1155CC), #DBDBDB, and not to leave out hex colors like #F9FAFA (which are also easy to remember).
I have tried colors pickers in Gimp, Photoshop and various online tools. For a color of my choice, I was never able to get a closer-looking color in the aforementioned "easy-to-type" hex format.
So, the question is, how do you do it?
The way I do it is to get the colors I want in a color picker, look at the hex values they generate, and then try to round to the nearest doubled pairs. So let’s assume I color-picked the following (and I typed these essentially at random, so only generate the actual colors at your own risk):
#82AC37
#B8AB29
#194645
In the first case, 82 is close to 88, AC is close to AA, and 37 is close to 33. So that one becomes #88AA33, or #8A3. Through similar means, I get #BA3 and #244.
If I find that pattern-rounding takes a color too far away from where it was, then I look for something with an easy-ish pattern, like (in the first case) #82AA33 or (in the second case) #B8A828. It becomes a bit of an art, really. And you definitely have to be comfortable with base-16, so that you can tell when it’s a better to round up versus down.