Answer:
The combination of a salicylate (aspirin) and ibuprofen (which are both NSAIDs) may increase the risk of gastrointestinal bleeding. It is advised to not take these two medications together at the same time, especially in high doses. If both medications are needed / required; Ibuprofen should be administered 30-120 minutes after, or at least 8 hours before, aspirin. It is also advised to talk to your doctor when combining these two drugs.
Also, aspirin and ibuprofen cancel out each others effects and shouldn't be taken together.
-Aspirin is taken to prevent heart attacks and strokes. Like ibuprofen it also relieves fever, pain and inflammation.
-Ibuprofen is taken to relive pain, fever and inflammation with less effect on platelets
According to the Mayo Clinic (related link) taking ibuprofen greatly reduces the benefits of daily aspirin therapy.
The best advice is almost always TALK TO YOUR DOCTOR.
If the use of both drugs is unavoidable, use aspirin first, then wait for 4 hours before using ibuprofen.