I'm taking online classes, but they don't qualify for a 1098-T statement. Can I still claim the tuition on my taxes?

Probably not. 

 To be eligible for the tuition credits, the course must be taken at "an eligible institution". The school should be able to tell you if it is an eligible educational institution. Schools that only offer online courses usually do not qualify.  Online classes taken at schools that also have  classroom instruction usually do count.

In general, an eligible educational institution is an accredited college, university, vocational school, or other postsecondary educational institution, including accredited, public, nonprofit, and proprietary (privately-owned, profit-making) postsecondary institutions. Additionally, in order to be an eligible educational institution, the school must be eligible to participate in a student aid program administered by the Department of Education. 

Enter your school at the link below, to see if it's on the dept. of education list.

   https://www.savingforcollege.com/eligible-institutions    https://ope.ed.gov/dapip/#/home

If you school is on the list, you probably qualify for an exception from the rule that you must have a 1098-T.  The exception question will come up after you tell TT that you did not get a 1098-T.

Possibly.  If you are attending an eligible educational institution and you otherwise qualify for the education credits, then yes, you would be able to claim a credit for your tuition paid.   if it is not an eligible education institution, then no, you would not be able to claim an education credit. 

Education credits - AOTC and LLC