"Oil pulling or oil swishing is a traditional Indian folk remedy that involves swishing oil in the mouth. It is mentioned in the Ayurvedic text Charaka Samhita, where it is called Kavala Gandoosha or Kavala Graha. Ayurvedic literature describes oil pulling as capable of both improving oral health and treating systemic diseases such as diabetes mellitus or asthma. While scientific evidence is lacking to support any systemic benefits of oil pulling, some studies have suggested that it may reduce oral plaque, halitosis, and gingivitis." [Wikipedia]The oil used to swish the mouth is typically vegetable based like sesame or sunflower and is performed for 15-20 minutes before being spit out (or swallowed depending on what you want to accomplish).
Though there are plenty of testimonials on the internet and explanations for its amazing effects including the oil's alleged ability to suck plaque off teeth, absorb germs into the oil, make teeth whiter, etc I feel the oil's effects are more mundane in nature.
Just as chapstick is an oil-based compound that treats dried and chapped lips by coating the surface allowing the lip mucosa to heal, oil pulling may just provide a protective barrier to provide a similar function. Oils are essential to skin and mucosal health and when such oils are stripped, problems occur (ask anybody who washes their hand with soap multiple times a day).
As such, I personally don't think it can hurt if someone wants to give oil pulling a try to address oral problems. But I would not recommend this type of unproven treatment to address systemic disorders like diabetes or asthma over more established medical management.
Of note, the references listed below are studies published in less-than-authoratative journals.
Tooth brushing, oil pulling and tissue regeneration: A review of holistic approaches to oral health. J Ayurveda Integr Med 2 (2): 64–8. doi:10.4103/0975-9476.82525.
Effect of oil pulling on Streptococcus mutans count in plaque and saliva using Dentocult SM Strip mutans test: a randomized, controlled, triple-blind study. J Indian Soc Pedod Prev Dent 26 (1): 12–7.
Mechanism of oil-pulling therapy - in vitro study. Indian J Dent Res 22 (1): 34–7. doi:10.4103/0970-9290.79971.
Effect of oil pulling on plaque induced gingivitis: a randomized, controlled, triple-blind study. Indian J Dent Res 20 (1): 47–51. PMID 19336860.
Effect of oil pulling on halitosis and microorganisms causing halitosis: a randomized controlled pilot trial. J Indian Soc Pedod Prev Dent 29 (2): 90–4. doi:10.4103/0970-4388.84678.