Ibuprofen
Ibuprofen is an analgesic commonly used in the civilian world to relieve pain, especially post-operative pain (in conjunction with other opiates), muscular aches and joint pain. It is a potent anti-inflammatory (specifically, it is a Non-Steroidal Anti-Inflammatory Drug), and not only reduces the sensation of pain but also works to reduce the cause of the pain itself.
It is especially useful from a modification perspective, as it seems to relieve the pain associated with puncture wounds (i.e. piercing) and skin trauma (i.e. tattooing), but is more commonly associated with countering inflammatory pain. It is safer than some analgesics, especially morphine-derived analgesics (e.g. codeine), and does not encourage bleeding in the same way that aspirin does.
It does, however, increase the risk of stomach ulcers (as do most NSAIDs), and it is very important (as with all other therapeutic drugs), to follow dosage instructions carefully.
Ibuprofen is often considered the non-prescription drug of choice for relieving pain caused by modification, due to its relative lack of side-effects (when taken as advised) and its effectiveness in suppressing modification-related pain. However, be sure to read the guidelines thoroughly. Do not take ibuprofen if you feel you may be at risk. In the event of side-effects, stop taking immediately and consult a doctor.