Windows Live is the online brand, all their free-download software/online services are "Windows Live X". I'm not sure how it cheapens it any more than if it was "Microsoft X" or "iProduct"...
Okay, I should rephrase: when I see Hotmail so prominently featured on the Windows Live ID page, I worry because of Hotmail's spammy past.
Also, the only times I've encountered Windows Live ID are times when it was being forced on me. E.g., when I got my broadband, I was forced to use a Windows-only CD to install a lot of (to me: irrelevant, useless, copycat) consumer software (photo sharing etc.), then get a Windows Live ID, and then finally activate the broadband.
So I pulled a Windows machine from a dumpster, did the install, got the Live ID, activated the broadband and then installed Linux. It felt dirty (and not from the dumpster).
After activation, the Live ID was not required, nor the software, nor Windows. So the whole experience was dictated and had no value for me, the customer.
EDIT: Apparently it only works on Windows, so I'll be sticking with Dropbox.
EDIT: Thanks, I had missed the Mac option. But to me, they cheapen their Live Mesh brand by association with Windows Live ID and Hotmail.