The applications can be categorized based on whether you study the sequence for analysis, or for DNA synthesis and assembly.
In addition to TF patterns mentioned in this answer, other patterns for DNA binding proteins, enchancers, promoters, and the Kozak sequence (
GCCGCC[A|G]CCATGG..) may also be useful for discovery of ORFs (genes) / regulation.
Certain methylase enzymes recognize a DNA pattern. For example EcoKI methylates adenine in
AACNNNNNNGTGC (2nd A) and its reverse complement,
GCACNNNNNNGTT (3rd A). Another such enzyme is EcoBI. This is useful for finding methylation sites, which may interfere with DNA restriction or expression.
Some restriction enzymes also recognize a DNA pattern: HinFI recognizes
Other such enzymes are EcoP15I, EcoRII. Finding these sites are very important for designing a DNA cloning or manipulation experiment.
For DNA synthesis, it is useful to avoid homopolymers (
N+) and repeated k-mers and hairpins (a sequence segment which has a reverse complement "nearby") as these can cause problems during synthesis.
Direct, tandem or inverted repeats can cause problems during cloning.
Finally, a perhaps trivial example is matching a polypeptide sequence, using DNA, as the genetic code is redundant. An example would be searching for target peptides in a protein.