Could alien life be based on something other than DNA?

Yes. Alien life could plausibly use something other than DNA to store and pass on hereditary information, though any life-like system would still need some way to preserve information, copy it with variation, and support evolution.

DNA is not the only chemically possible genetic molecule. Scientists have studied alternatives such as RNA-based systems and synthetic “XNA” molecules, where the sugar-phosphate backbone or bases differ from DNA. These show that heredity-like chemistry is not limited to DNA exactly.

That said, DNA is extremely effective in Earth conditions: it is stable, information-rich, copyable, and works well with proteins and RNA. So if alien life is water-based and carbon-based, it might use DNA-like chemistry even if not identical DNA. In more exotic environments, life might use a different information polymer, a different solvent, or a radically different biochemical system—but those ideas are more speculative.