CAGCAGCAG would be the direct repeat of a CAG triplet repeat. AAAAAxxTTTTT would be a short inverted repeat. Direct repeats can align out of register in duplex DNA, whereas inverted repeats can pair with themselves along the same DNA strand, forming hairpins and cruciforms. For these reasons, both direct and inverted repeats can form DNA conformations that differ from the usual duplex B-form. Other direct repeats, such as multiple CGs, can form a left-handed Z-DNA. There is abundant literature on the involvement of triplet repeats, and their propensity to expand in number, and other repeats in human disease, particularly neurological diseases. The Y-chromosome contains very large inverted repeats with repeated copies of genes, and this organization is thought to be important for maintaining the stability of these sequences in the absence of a homologous chromosome. There is substantial literature on this subject as well.
If two separate direct repeats recombine with one another - in a process similar to crossing over - the intervening DNA is deleted. Recombination between inverted repeats results in inversion of the intervening DNA segment. Recombination between repeats on different chromosomes can cause translocations.