There are a few rules that are common to most casinos, however, they are primarily to discourage common methods of cheating or any outward gang affiliation.
Bandannas and skullcaps are generally prohibited by most locations.
Shirts with vulgar printing or see-through fabric are generally unacceptable, as are extremely short shorts. 
If there is a pool resort in the same building as the casino, bikinis and other swimwear are usually not allowed on the floor.
Large bags, such as duffle or gym bags are usually not allowed. Large purses are usually not prohibited, but they can look suspicious and may need to be searched before you can bring them onto the floor.
American casinos generally favor a casual dress code. Provided you are cleanly and inoffensively dressed, you should be alright. European and Australian casinos may also be casual, but they tend towards a smarter style of dress.
The more upscale casinos may require a jacket for men and a dress, skirt, or another formal outfit for women. Be sure to do a little research before you go, since almost all casinos will post their dress code on their website.
While a wide range of outfits may be acceptable on the floor, keep in mind what else you may be doing that evening.
If you intend to visit one of the upscale restaurants, attend a show, or enter one of the clubs that are frequently inside or near casinos, you will need a higher class of dress, and you might as well wear your more upscale outfit to the casino.
While casual clothes are often acceptable, keep in mind that how you dress can also affect how you are treated.
A t-shirt and jeans might get you in the door, but a sharp suit or dress will get you noticed.
This can often result in a much better experience at the casino. In addition, dressing up gives a trip to the casino more gravitas, can help you have a better time, and leaves you better prepared should the night take you to a local club or five-star restaurant when the gambling is done.
