Liquid latex is a standard theatrical and costume product, used in items ranging from facial prosthetics to paint-on clothing. If you can't get latex or have a latex allergy, you'll need to find a substitute. The best replacement depends on your planned use for the latex.
Silicone casting rubber is a favourite material to use as a substitute for latex in prosthetic make-up work. Silicone is widely considered to be superior to latex and more closely resembling human flesh in texture, weight and movement. In addition, silicone is hypoallergenic and safe for those with latex allergies. The major drawbacks of silicone are its increased expense and the fact that it's more difficult to work with. It requires practice for good results.
If you're looking for a substitute for latex as used for a prosthetic adhesive, try spirit gum. Spirit gum is an amber liquid adhesive made from alcohol and resin. Compared to latex, it creates a more secure hold with less bulk, but it's more difficult to remove from skin. To fully clean it from yourself and from the prosthetics, you'll need a specially made adhesive solvent. Spirit gum may induce allergies in some, but it has no latex in its make-up and won't trigger a known latex allergy.
Liquid latex is commonly used in the creation of fake wounds, but if you can't use latex, you can substitute another material commonly used for this purpose -- wax. Wherever costume make-up is sold, you can usually find a soft, beige putty with a wax base intended for building ridged scars and wounds on skin, to be painted with stage make-up and filled with fake blood. Wax wound putty has an advantage over latex in that it's easier to shape with precision. However, it's less durable and you have to be careful not to press or smear it while wearing it.
One popular, non-theatrical use of liquid latex is as a fashion statement, often associated with club scenes and alternative lifestyle activities. Coloured latex is painted directly onto skin, there to harden into a flexible, ultra form-fitting body covering. To create a similar effect without latex, try an alcohol-based body paint. This is the stuff used by professional movie make-up artists to colour skin. It will last for days. Combine it with small patches of vinyl or vinyl garments for areas on your body that might need a little more paint coverage.