What's the most efficient file format for the storage of DNA sequences? I'd like to learn which format is most commonly used for storing the full human genome sequence (4 letters without a quality score) and why.

I assume that storing it in plain-text format would be very inefficient. I expect a binary format would be more appropriate (e.g. 2 bits per nucleotide).

Which format is most common in terms of space efficiency?
Genomes are commonly stored as either fasta files (.fa) or twoBit (.2bit) files. Fasta files store the entire sequence as text and are thus not particularly compressed. 

twoBit files store each nucleotide in two bits and contain additional metadata that indicates where there's regions containing N (unknown) bases.

For more information, see the documentation on the twoBit format at the UCSC genome browser.

You can convert between twoBit and fasta format using the faToTwoBit and twoBitToFa utilities.

For the human genome, you can download it in either fasta or twoBit format here: http://hgdownload.cse.ucsc.edu/goldenPath/hg38/bigZips/