My answer is “None.”
There is no compelling reason to perform single-incision laparoscopic surgery (SILS).
Take cholecystectomy, for example. The three 5 mm incisions in the upper abdomen done for standard laparoscopic cholecystectomy are nearly painless and, after a few months, almost always become invisible. The umbilical incision is larger and does cause pain, but the incision for SILS is generally 50% larger than that of standard laparoscopic cholecystectomy and likely to be just as painful if not more so.
For appendectomy, the same reasoning applies regarding the two 5 mm incisions and the umbilical incision. Not only is the umbilical SILS incision larger, one recent paper reports that it results in more postoperative pain too.