It depends a little bit on what type of sequences, and how perfect you want your matches to be. The most comprehensive database for DNA sequences would be the "nucleotide collection nr/nt" database, which is listed under "Other" at the NCBI BlastN suite. For particular searches you might also get very good results by using the "NCBI genomes" database, which is also listed under "Other".  

Use NCBI blast search to know the  similarity.

all the best

NCBI BastN with nr/nt database would be enough good. Be careful with results interpretation. such short sequences can have a vast number of homologs by chance. It will have a sense when:

- you make search against narrow group of organisms,

- you fragments represent unique strings of DNA.

- your fragments have regulatory function and conserved across many different genomes

To search for short DNA sequences, you can use more specific tools such as GLsearch that try to find your query as a whole in the database sequences :

http://www.ebi.ac.uk/Tools/services/web/toolform.ebi?tool=fasta&program=glsearch&context=nucleotide

For the database, it depends what you want to see and where does your sequences come from. You can restrict to coding sequences, for exemple.