Is there DNA/genetic similarity between life-forms ?

Hi,

Has there been found any correlation in genetics between the form of an
organism and it's DNA ? Do similar forms of life end up with similar DNA ?
What if two species that have very similar forms, originally had very
different ancestors, but through evolution ended up with a similar current
form. Would they have more similar DNA or not ?

In other words, does nature tend to optimize towards the same solution in
genetic terms, when it tries to fill the same evolutionary niche ? (Even
when starting from a different point of origin).

Thanks,
Rob