I hit a similar issue with my site when developing some responsive CSS. I wanted any embedded Youtube objects to resize, with aspect, when switching from the desktop CSS to something smaller (I use media queries to re-render content for mobile devices).
The solution I settled on was CSS and mark-up based. Basically, I have three video classes in my CSS thus:
.video640 {width: 640px; height: 385px}
.video560 {width: 560px; height: 340px}
.video480 {width: 480px; height: 385px}
…?and I assign one of these to the Youtube content I include, depending on its original size (you may need more classes, I just picked the most common sizes).
In the media query CSS for smaller devices, these same classes are simply re-stated like so:
.video640 {width: 230px; height: 197px}
.video560 {width: 230px; height: 170px}
.video480 {width: 240px; height: 193px}
I appreciate this requires some mark-up "up-front" when including videos in your HTML (i.e. adding a class), but if you don't want to go down the Javascript route, this works pretty well -- you could re-state your video classes for as many different sizes as you require. Here's how the Youtube mark-up looks:
<object class="video640" type="application/x-shockwave-flash" value="YOUTUBE URL">
<param name="movie" value="YOUTUBE URL"></param>
</object>
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