Although I do have a group of friends that I usually travel to Vegas with, I also take a couple solo trips a year, fitting them in here & there at the last minute if my work schedule permits. I absolutely LOVE going on my own for the same reasons previous poster's have mentioned - no one to slow you down, no need to make sure you are doing things the other people are interested in, and the ability to have a totally "me" oriented schedule! What a treat!
You can get excellent last minute tickets to many of the best shows in town when you only need a single seat. I've also met many great people in restaurants while dining solo - seems like someone is always willing to start a conversation and often they will ask you to join them!
Vegas is one of the few places that are just perfect for the solo visitor. Since groups that travel there together are often separated anyway due to their individual interests, it is quite common to see a single person dining, attending shows, sitting at a casino table, etc. You won't feel out of place at all.
As a woman, it is one of the places where I feel quite safe being out and around at all hours of the day or night. I do exercise common sense & choose my routes with attention to remaining in busier areas and I will take a cab if I don't feel comfortable walking in certain areas. As a result, I've had minimal issues with personal safety while on my own.
Edited to add: Another bonus is that the time share folks leave you alone when you're solo - they always zero in on the couples!