When I do Abhyanga (Indian warm oil massage, which uses A LOT of oil) I always wipe the client down afterwards. I don't wipe each body part down, though. I massage their front side and then have them turn over. The sheet against skin absorbs most of the oil from the front side. After doing their backside, I do wipe down the legs, gluts, back, arms and neck. However, everyone coming to this treatment knows it is completely oily and I also have a shower they can use afterwards. (I also use a waterproof table cover to protect my padding/table)
When I do a regular swedish/deep tissue massage, I do use oil. It is an oil that washes out of clothing easily (Soothing Touch Fragrance Free Lite). I use a medium amount of it. Not a lot, but not very little. I think they are pretty oil free when I am done, but I live in a very dry climate and many times when I try to wipe the oil off they say "No, leave it on!" In any case, for every client, I wipe the feet off with hot towels (I use cream on the feet) and then put some special Amber Heel Recovery cream on their feet.
I have been thinking recently of creating a "Preferences Form" for my regular clients that asks specifically about their likes and dislikes regarding music, draping, oil, lotion, cream, style of treatment, or anything else I can think of. I know a lot of this stuff about them already, but it would be nice to have directly from them in a chart in their file.
I use an Ayurvedic approach in general and that states that oil is good and a healing, medicinal element. I know not everyone likes oil, but I also think that many who can come to understand this, learn to like it ("excess" oil) a lot. For those that don't, I always abide by their wishes and use lotion/cream and/or wipe them down and/or offer a shower.