Injuries cause the release of prostaglandins and therefore cause pain. Prostaglandins are potent vasodilators and pro-inflammatory compounds that cause the erythema (redness), pain, and hyperemia (increased blood flow) associated with trauma or oral tissue damage.
  The enzyme cyclooxygenase converts arachidonic acid to prostaglandins and thromboxanes.
  Prostaglandin-synthesis inhibitors (PSI) include acetaminophen (Tylenol), ibuprofen (Motrin), and aspirin. PSIís reduce
pain because they interfere with the function of the enzyme cyclooxygenase.

See also:

A SideBar on Sensitivity to Pain

NSAIDs (Non Steroidal Anti-Inflammatory Drugs)
The most common of these are Aspirin, Ibuprofen, Acetemenophen (Tylenol), and Naproxen

Ibuprofen cross-effects:
Note especially that Copper supplementation appears to increase the effectiveness of NSAIDs and aspirin.
Iron supplementation may be appropriate, to counter Iron loss from Ibup. (and aspirin) use.
The flavonoids found in the extract of licorice known as DGL (deglycyrrhizinated licorice) are helpful for avoiding the irritating actions NSAIDs and aspirin have on the stomach and intestines.

"Although aspirin reduces swelling, pain, and fever just like NSAIDs, it is classed (by some) as a member of the salicylate family of drugs."
Supplements which may be indicated with aspirin include Folic Acid, Vitamin C, and Zinc (see also note on Copper, above).  Vitamin E may increase bleeding in conjunction with Aspirin, but that is not well demonstrated.    (Folic Acid excretion in urine is seen in rheumatoid arthritis patients, even without Aspirin intake, so supplementation at 4oomg is indicated.)

Aspirin/Ibuprofen/Tylenol effects and uses; Aspirin chemistry

More info on NSAIDS and Salicylates - Side effects and cross effects

Anti Cancer effects - The nonsteroidal anti-inflammatory drugs aspirin and indomethacin attenuate -catenin/TCF-4 signaling
Increasing epidemiological and experimental evidence implicates non-steroidal anti-inflammatory drugs (NSAIDs) as  anti-tumorigenic agents. The precise mechanisms whereby   NSAIDs exert their anti-neoplastic effects remain poorly understood. Studies from hereditary and sporadic colorectal  cancer (CRC) patients suggest that NSAIDs may interfere with initiating steps of carcinogenesis

Enough Ibuprofen at the wrong time may block aspirin's ability to protect against heart attacks
Ibuprofen and other Cox-1 (cyclooxygenase) inhibiting NSAIDs may block aspirin's effects on platelet activity, which is the source of aspirin's heart/circulatory benefit.  The mechanism is through binding by the NSAID to the COX-1 enzyme, preempting the ability of aspirin to do so.   However, taking the aspirin two hours before the ibuprofen permits the aspirin to preempt the binding, and so preserve the effectiveness of the aspirin regime in protecting the heart.   Unfortunately, repeated (3 or more a day) use of  a COX-1 NSAID such as Ibuprofen has been shown to leave enough of the drug in the system to prevent the aspirin binding.   (Link)

(Result = Take no more than 2 NSAID (Ibuprofen) a day; start with the "heart" aspirin, take the first Ibuprofen at least 2 hours after the first aspirin; take the second 6-8 hours after the first.   For the "usual" third dose of Ibuprofen pain relief, substitute an aspirin (or two) 6-8 hours after the second Ibuprofen,

Common Painkiller Cuts Heart Benefits of Aspirin
"When patients taking aspirin for cardioprotection require chronic treatment of inflammation with an NSAID, the addition of diclofenac or a conventional selective COX-2 inhibitor would seem preferable to ibuprofen,"

Ibuprofen belongs to a class of drugs known as non-steroidal anti-inflammatory drugs (NSAIDs). They relieve pain by blocking the action of an enzyme called Cox-1, which is found in the stomach and the blood, and Cox-2, which is in the skin and joints and is also produced at the site of a wound or pain.

COX-2 Inhibiting (COX-1 sparing) NSAIDs

celecoxib = Celebrex (Rheumatoid and Osteoarthritis) <se kidney damage, gastrointestinal ulceration>
Rofecoxib = Vioxx (Osteoarthritis) <se liver damage? heart?>  [Rofecoxib studies in OA patients showed no differences with
Diclofenac and Ibuprofen as far as efficacy, less adverse events and less withdrawal rates]
diclofenac = <se gastrointestinal ulceration>
valdecoxib = Bextra (Lupus) <se skin diseases Stevens-Johnson syndrome, toxic epidermal necrolysis and exfoliative dermatitis>

Experimental evidence has shown that COX-2 promotes survival of colonic adenomas  and colonic cancer as well as its expression is associated with the deposition of  beta-amyloid protein in Alzheimer's disease; COX-2 inhibitors may find utility in the prevention or treatment of these conditions but human studies have to corroborate the in vitro and in vivo findings

Other drugs side effect information:
acetaminophen = Tylenol <se liver damage>
aspirin = var. <se gastrointestinal bleeding>
naproxen = <se gastrointestinal ulceration> <Vioxx users had half the rate of ulcers and bowel perforations as those taking naproxen>

<arthritis sufferers who have had ulcers should not take either Pharmacia/Pfizer's arthritis drug Celebrex, nor AstraZeneca's ulcer medication Prilosec ... in combination with the generic anti inflammatory drug clofenac.>