Skin tags will not go away on their own.
More Info: Though skin tags do not disappear on their own, they skin tags have been known to fall off through the same act of friction that caused them in the first place. 
Should I Have a Skin Tag Removed?
Skin tags are generally benign and other than cosmetic reasons generally do not need to be removed. In some cases where the skin tag is in a sensitive area or is continuously rubbing against clothing, they can become irritated and sensitive and may become uncomfortable. In these cases your doctor may recommend removal.
Procedure to Remove Skin Tags
There are several medical procedures performed to remove skin tags. Most cases are fairly simple with little discomfort and can be performed right in the doctor’s office under local anesthesia depending on the size of skin tag. Some options include medically tying or cutting off the tag with surgical scissors, freezing the tag, or burning it off.
Home treatments should not be attempted for two important reasons. First, a medical professional should diagnose a skin tag because it does often mimic other skin conditions, which means that just because a skin tag is benign, doesn’t mean you have a skin tag. Second, the risk for infection is high if you attempt to remove a skin abnormality yourself.
“Skin Tag.” MedicineNet.com. N.p., n.d. Web. 23 May 2011. <www.medicinenet.com/skin_tag /article.htm>
“Cutaneous skin tags – PubMed Health.” National Center for Biotechnology Information. N.p., n.d. Web. 23 May 2011. http://www.ncbi.nlm.nih.gov/pubmedhealth/ PMH0001851/