If Skype is updating, it'll do it from within the program, like yours did.
That's legit, this is a plain text email that tells you to click on a link in the email to update. The link even looks legit, but it's not.
In the case of the Adobe reader update, it wanted you to go to
...adobe-reader10-center.com (note: I got the email 5 times and there were variations in this address.)
In the case of the purported Skype update, it wanted you to go to
...skype-update-center.com
There were also notable giveaways to the scam, such as the return address had Adobe Systems Incoporated (note misspelling of Incorporated) and other errors in grammer and spelling that are dead scam giveaways.
If you see these emails, also do NOT type the url into a browser and go there, the results will be the same, you'll be into the scammer's system. If you do go there and download the proferred "update" your PC will be infected by trojans, keyloggers, viruses or other nefarious programs.
If you feel like you need an update to Adobe Reader, they're always available for free at www.adobe.com. Skype will update from within the program, automatically.