YouTube has recently enabled High Quality/High Definition videos in the embedded player. That is, when there is a high quality version of a video available, you get the chance of switching to it, although by default, movies will still play in the default quality. All over the net, you can find instructions on how you can force the embedded player to show the HD movie by default. What most (if any) of these pages do not tell you, is that this will not work with versions of Flash below 9.0r115.
I found out the hard way (customer asked me to enable HD movies, only to then later complain he could no longer view the movies on his own site) that users of Flash 9.0r115 and up will get a crisp, high quality movie, but users of older versions get to look at the "revolving balls" that indicate the movie is being loaded from YouTube. Indefinately.(Disclaimer: I only tested on Windows, the version for Windows directly below r115 that Adobe supplies in their "archived versions pack" is r47. There is also an r48, which appears to only be available for Linux, which I have not tested. However, I expect the results will be the same).
Unfortunately, I could not find an overview of installed flash versions any more detailed than this overview from Adobe. At the time of writing, it shows around 98-99% market penetration of Flash versions compatible with Flash 9, whereas Flash 10 is only 55-60%. Although this doesn't tell us much about how many of those Flash 9 players are actually >=9.0.115, it does show us what we really already knew: people are not very loyal upgraders.
If you have Google Analytics or a similar analysis tool of your website's traffic and visitors, it can tell you what versions of Flash your visitors are using. I did the math for a large Dutch site I run which, in terms of computer equipment, I would say is fairly representative of the Internet-going public in Holland (i.e. it is a site unrelated to computers and technology). All versions below Flash 9.0r115 amounted to 9,67%. (Flash 10 acceptance is a little bit below Adobe's quoted figure, 51%). This is actually not too bad (I expected worse), but it still amounts to almost 10% of your sites visitors that would not be able to view the YouTube movies on your site which you equip with the infamous "&ap=%2526fmt%3D18" at the end of the URL.
You could of course install something that asks your users to upgrade if they have an older version. I don't have any experience with that (I did see mention of Adobe having an upgrade kit available, that can help you nudge your site's users to upgrade), but I have my doubts whether it is worth the hassle for you and your users, considering the added functionality is nice, but in most cases not extremely important (don't forget that users will still be able to switch to the high quality version of your movies manually, within the embedded player).