A study into whether or not videogames, along with other electronic media and devices, cause headaches or migraines in adolescents ultimately determined that there was no link between the two.
Medical News Today details the study (PDF), which queried 1,025 kids between 13 and 17 years of age. 489 of those interviewed claimed to suffer from headaches, while the remaining 536 indicated no such affliction. Comparing the groups, researchers found no deviation between the two when it came to television viewing, electronic gaming, mobile phone usage or computer usage.
The study concluded:
With respect to the current debate on adverse health effects of electronic-media use, we cannot point to systematic effects of single media types nor on specific types of headache which might predominantly be caused by the use of electronic media.
The study did suggest a casual link between daily music intake and headache suffering however.