In terms of general crime safety - meaning trying to avoid getting yourself killed, mugged, etc. - you're usually okay if you stick to the high-profile tourist areas. The Strip, Fremont Street in the Downtown area, and the individual casinos and attractions scattered throughout the rest of the city are, for the most part, very safe places. Police and security presence is high and the number of cameras recording every inch of the major hotels seems to be effective in keeping all but the most brazen of criminals at bay.
However, most of those tourist areas are surrounded by neighborhoods that are questionable at best and downright scary at worst. Just as you probably wouldn't go wandering around the dark streets of your nearest major city at night, you should never wander too far away from the bright lights of The Strip or Downtown when you are in Vegas.
If you're driving and have to pass through some of these questionable neighborhoods, always be sure you know where you're going before you start the car and keep your doors locked, especially at night. I know this is common-sense stuff but it bears repeating here.
If you're getting a rental car, make a request ahead of time for one that does not bear any stickers or placards declaring it as such. Although I haven't heard of this being a major issue in Vegas, there have been incidents in other cities of criminals targeting people in rented cars so it can't hurt to take this simple precaution.