Minimum 2 days is fine but the maximum is really 5 days. Spending an entire week in Las Vegas is a really bad idea. They say it's like New York where after a few days you're overwhelmed and ready to just leave.
Las Vegas can be fun but it can also be overrated. It is a gambling mecca or a gambling capital. It can be a great place if you're a professional poker player but keep in mind this is the kind of lifestyle you're going to have to get used to.
So if you're planning a trip do your research and see if you're getting the absolute best deals on your hotel and get as many comps as possible. You're crazy not to do this. Once you get on the mailing list you'll see the offers come flooding in but remember no more than 5 days in Las Vegas