I can't test it, but I see that it uses character set win-1251.
Perhaps for Cyrillic the following is also possible:
Character set: koi8r
In general I would say: Latin-1 iso-8859-1 is preferred for OpenBiblio.
For experimenting with other scripts, UTF-8 seems the right choice. But when producing labels or letters with the reports system, the PDF might show strange characters (there is a partial fix, linked at the bottom of this message). For using UTF-8, I think you should adjust the following:
Character set: utf-8
tab Admin, Library Settings, HTML Charset: utf-8
UTF-8 case sensitive (Florian)
When testing UTF-8, I was also experiencing what Florian reported: search is case sensitive for some characters.
Probably this is not an issue in OpenBiblio because i get the same result in a command line interface to MySQL (5.1.41). The following doesn't find niño
select * from biblio where biblio.title like '%NIÑO%';
Strange characters in PDF reports
PDF's produced by OpenBiblio's reports system probably will not be very useful for Cyrillic users. You can try the fix linked below.