The American Opportunity Credit (AOTC) replaced the Hope Credit.
You could only ever take two years of the Hope Credit, which the AOTC has expanded to four.
You would only have been able to claim the Hope Credit in 2008 or before - from 2009 to present, the AOTC would take its place.
For prior years: If you don't see Form 8863, there was no way to claim any refundable or nonrefundable credits that year.
Also, The IRS is only ever concerned with knowing if you've claimed this credits for 4 total years -
eligible years do not have to be consecutive. (Form 8863, line 23)
Example: You claimed the Hope Credit for 2006 and the AOTC for 2012. You would indicate you claimed 2 years of the Hope/AOTC credit.
Read more about tax benefits for education expenses