I know that not everyone is aware of, or has had any experience with
other dialects of Old Norse, but here is one often neglected Old
Swedish (Old West-Gautish, to be precise) text, the first extant text
in Old Swedish.
http://books.google.com/books?id=aZgyAAAAIAAJ&printsec=titlepage&dq=editions:05VFRSSnJBX2k4sx#PPP7

I have a translated "edition" of the most famous section (found in
Gordon's "Introduction to Old Norse") of The Older West-Gautish (or
Geatish) Law on my school webpage. My undergraduate senior thesis was
a translation, with full introduction, commentary, glossary, and
bibliography.
http://www.tc.umn.edu/~pete2581/Complete%20Project%20(Word%202003).pdf

I encourage anyone who has learned a significant amount of Old Norse,
that is primarily Old Icelandic, to read some texts from other
dialects, like the one I'm providing above. Also, there is Gutasaga
and Gutalag for an even more strange East Norse dialect. Let me know
what you all think. I am a graduate student in Germanic medieval
studies, and my next major thesis will probably be on a comparison of
the Older West-Gautish law with Grágás (which is incredibly lengthy)
by comparison, as well as a significant commentary on pre-Christian
Scandinavian and Germanic legal tradition. Let me know what you all
think. Í friði,

Paul