There are studies on cupping, but many are of poor quality, published in alternative medicine journals, and mostly done in East Asia--which can influence the results. The short version, is that there is some evidence for efficacy of cupping for specific conditions. But the results are not very rigourous. For example, Zhen Jiu Lin Chuang Za Zhi (Clinical Journal of Acupuncture & Moxibustion) publishes studies like these, which look like science, but have conclusions like:
Bleeding the tips of the ears clears heat and resolves toxins, frees the flow of the channels and quickens the blood. Bleeding Da Zhui followed by cupping disperses welling abscesses and scatters binding or nodulation, quickens the blood and stops pain, dispels stasis and eliminates evils. As the authors point out, Da Zhui is a transport point on the governing vessel as well as a meeting point of the governing vessel and the hand and foot three yang channels.
For more reasonable examples see:
J Occup Health. 2012;54(6):416-26. Epub 2012 Sep 1. "Cupping for treating neck pain in video display terminal (VDT) users: a randomized controlled pilot trial." Kim TH, Kang JW, et.al.
This was a randomized controlled pilot trial to evaluate the effectiveness of cupping therapy for neck pain in video display terminal (VDT) workers [...] Two weeks of cupping therapy and an exercise program may be effective in reducing pain and improving neck function in VDT workers.
Am J Chin Med. 2012;40(2):269-77. "The effects of wet cupping on coronary risk factors in patients with metabolic syndrome: a randomized controlled trial." By Farahmand SK, Gang LZ, et.al.
This study aimed to determine the effects of wet cupping on lipid profiles and anthropometric characteristics of patients with metabolic syndrome [...] Wet cupping does not have a significant effect on anthropometric or biochemical indices compared to the effect of dietary advice alone.
Perhaps the most comprehensive review on the subject is PLoS One. 2012;7(2):e31793. doi: 10.1371/journal.pone.0031793. Epub 2012 Feb 28. "An updated review of the efficacy of cupping therapy." By Cao H, Li X, Liu J.
Six databases were searched for articles published through 2010. RCTs (Randomized Control Trials) on cupping therapy for various diseases were included [...] 35 RCTs published from 1992 through 2010 were identified. The studies were generally of low methodological quality. Diseases for which cupping therapy was commonly applied were herpes zoster, facial paralysis (Bell palsy), cough and dyspnea, acne, lumbar disc herniation, and cervical spondylosis [...] Meta-analysis showed cupping therapy combined with other TCM treatments was significantly superior to other treatments alone in increasing the number of cured patients with herpes zoster, facial paralysis, acne, and cervical spondylosis [...] This review showed that cupping has potential effect in the treatment of herpes zoster and other specific conditions. However, further rigorously designed trials on its use for other conditions are warranted.
Based on this literature review, I would conclude that cupping research is dangerously close to being a pseudo-science. I was not able to find any studies in mainstream journals like the New England Journal of Medicine or the British Medical Journal.
†Please note that this answer does not constitute medical advice. It is only meant to summarize published research related to the original claim and limited to the cited sources. Consult your physician about what these results may mean for your health.