When I use one of the default styles in biblatex, Unicode characters are correctly printed in the bibliography. When I use the biblatex-apa package, on the other hand, (adding the option style = apa when loading the biblatex package), many fields display these characters as jibberish sequences, but other fields display them correctly. Here's an example:
\documentclass{article}
\usepackage{fontspec,xunicode,xltxtra} % XeLaTeX
\defaultfontfeatures{Mapping=tex-text} % support TeX conventions like ``--''
\setmainfont{Linux Libertine O}
\usepackage[american]{babel}
\usepackage{csquotes}
\usepackage[style = apa, backend = biber ]{biblatex}
\DeclareLanguageMapping{american}{american-apa}
\addbibresource{test2.bib}
\begin{document}
Clearly Bj{\char"00F8}rn V{\char"00E5}ge likes the letters {\char"00E6}{\char"00F8}{\char"00E5} a lot \parencite{author1}.
\printbibliography
\end{document}
My .bib-file:
@ARTICLE{author1,
AUTHOR = "Bj{\char"00F8}rn V{\char"00E5}ge",
TITLE = "A title with {\char"00E6}{\char"00F8}{\char"00E5}",
JOURNALTITLE = "The {J}ournal of {\char"00E6}{\char"00F8}{\char"00E5}",
YEAR = "2011",
ADDENDUM = "An addendum with {\char"00E6}{\char"00F8}{\char"00E5}",
ANNOTATOR = "The annotator is {\char"00E6}{\char"00F8}{\char"00E5}",
COMMENTATOR = "The commentator is {\char"00E6}{\char"00F8}{\char"00E5}",
EDITOR = "P{\char"00F8}lsa S{\char"00E6}b{\char"00F8}",
ISSUE = "The issue of {\char"00E6}{\char"00F8}{\char"00E5}",
ISSUETITLE = "The issuetitle is {\char"00E6}{\char"00F8}{\char"00E5}",
ISSUESUBTITLE = "The issuesubtitle is {\char"00E6}{\char"00F8}{\char"00E5}",
JOURNALSUBTITLE = "The journalsubtitle is {\char"00E6}{\char"00F8}{\char"00E5}",
NOTE = "The note says {\char"00E6}{\char"00F8}{\char"00E5}",
NUMBER = "5",
PAGES = "100--200",
SERIES = "The series of {\char"00E6}{\char"00F8}{\char"00E5}",
SUBTITLE = "The subtitle is {\char"00E6}{\char"00F8}{\char"00E5}",
TITLEADDON = "The titleaddon is {\char"00E6}{\char"00F8}{\char"00E5}",
TRANSLATOR = "The translator's name was {\char"00E6}{\char"00F8}{\char"00E5}"}

{\char"00E6}{\char"00F8}{\char"00E5}instead ofæøåin thebibfile? – Håkon Malmedal Aug 1 '12 at 18:06biblatexearlier, and the pdf produced black boxes. – Sverre Aug 1 '12 at 18:09æøåin the bib file and had no problem. – Håkon Malmedal Aug 1 '12 at 18:12biblatex-apanot being able to parse Unicode codes in some fields. I prefer defining my characters in terms of their Unicode codes, cuz then anyone can open my.texand.bibfiles on any computer with any fonts, and know exactly what characters I intend to be displayed. That's a big deal in my field. Plus I use a lot of characters you can't just type on the keyboard. – Sverre Aug 1 '12 at 18:37