The installation of ceramic tile requires a smooth, flat surface, so you can only install it over noncushioned vinyl. If the sheet vinyl is padded or has a layer of padding beneath it, the ceramic tile will eventually warp and shift out of place.
Peel-and-stick vinyl tiles can be placed over sheet vinyl as long as the glue on the backside of the peel-and-stick tile adheres to the sheet vinyl; you may need to lightly sand the sheet vinyl to ensure a tight bond. If your sheet vinyl contains asbestos, it isn't advisable to sand the surface, and you may need to hire a professional to remove the sheet vinyl.
Synthetic- and real-wood flooring can be installed over sheet vinyl, as long as the sheet vinyl is directly attached to the subfloor and there's no padding in the vinyl--most types of hardwood require a flat foundation and will bend and warp if installed on a padded surface. If the wood planks require glue or other adhesives, you must first lightly sand your asbestos-free sheet vinyl. You can nail wood-plank flooring onto the sheet vinyl as long as you don't mind that the sheet vinyl will forever be damaged.
Carpet is one of the easiest ways to cover sheet vinyl. You can place carpet padding over the sheet vinyl, then install the carpet. Carpet is also easy to remove if you ever decide to remove the sheet vinyl or install a different type of flooring in the future.