ResearchGate link for the article mentioned by Michael Lauck:

https://www.researchgate.net/publication/51980539

Article A Viral Discovery Methodology for Clinical Biopsy Samples Ut...

Thank you Michael and David. I just read the article, it could be very useful.

You have three options:

* Human DNA depletion

* Viral DNA enrichment

* Extremely deep sequencing

To expand on that third one, as an alternative to enrichment/depletion you can genotype on a platform where even 1% of the sample containing viral DNA is going to produce meaningful results (e.g. a 600Gbp-1000Gbp run on an illumina HiSeq).

I did a bit of web searching, and came up with a couple more specific solutions:

Here's someone else who has done cheap human DNA depletion with some success, testing CF11 cellulose columns against Lymphoprep (a sucrose density gradient filter):

http://www.malariajournal.com/content/pdf/1475-2875-11-41.pdf

I guess the idea behind the Lymphoprep method [http://www.stemcell.com/en/Products/All-Products/Lymphoprep.aspx] is that you filter out the human cells by size, and hope that there's enough extracellular virus floating round for subsequent genotyping.

There's also a NEBNext Microbiome DNA enrichment kit, which filters out host DNA. It apparently works by capturing methylated DNA (essentially absent in viral / bacterial populations):

https://www.neb.com/products/e2612-nebnext-microbiome-dna-enrichment-kit

Presumably there are similar kits from other manufacturers.

Another approach is the Virochip, e.g.:

https://www.researchgate.net/publication/51114072

While this will not identify completely uncharacterized viruses, it will detect many known and closely-related viruses. There are always potential pitfalls with this or any other approach, though...see the sad story of XMRV.

Article Using a Pan-Viral Microarray Assay (Virochip) to Screen Clin...

Thank you David, Kenneth and Rohan! All the suggested solutions were interesting for me, especially the NEB kit. Thank you very much.