I've always preferred YYYY.MM.DD, this way you can sort things very easily. If you write the names of the months, it doesn't translate well to other languages, though it may be similar, *AND* more importantly from a geek perspective, if you do a sort, April shows as the 1st month of the year, before January - not good.
All depends on what you want. YYYY-MM-DD (or variations, including YYMMDD) are good when there is a chance it could be needed to be sorted.
If you do the reverse DD.MM.YYYY you can't sort it either since the 1st day of every month shows up 1st. Dumb. Friendly to non-geeks, but dumb.
However, not all data are to be sorted. There are some applications where friendliness to non-geeks is more important than sortability (eg, when showing only one value anyway). Sometimes we have to sacrifice something to the users to get them out of our hair.
The worst annoyance I've seen is using Unix time as a timestamp on log dates. It's the most unreadable of all formats. Sorts nicely though, but what a bitch to read. (Unix time being the number of seconds in decimal since 1/1/1970.)
The logs are usually intended to be human-readable. However, as long as it is reasonably trivial to write a program to process the timestamps, it's merely annoying.