Here are some sites that I've found useful.
Old Norse Online (Todd B. Krause and Jonathan Slocum; 10 lessons +
grammar + runes)
http://www.utexas.edu/cola/depts/lrc/eieol/norol-TC-X.html
If you're new to grammatical jargon, the lessons at Norse Course
homepage are probably a better place to start, but once you get your
bearings this is great. And you can always delve into the
historical & cultural background information that sets the scene
before each reading excercise. And no fiddly tests or words to look
up: it explains everything as you go along!
(Old Norse Online) Bibliography
http://www.utexas.edu/cola/depts/lrc/eieol/norol-E.html
Learning Old Norse
Some Suggestions (links, but some broken, and book recommendations)
http://has55.www9.50megs.com/OldIcel/LearningOldNorse.html
Arild Hauge's runes
http://www.arild-hauge.com/eindex.htm
Mentalcode Icelandic (introduction to Modern Icelandic + information
on how to type Icelandic characters on computers)
http://www.mentalcode.com/nl/islenska/index.page
DICTIONARIES & REFERENCE
Zoega's Old Icelandic Dictionary
(which Patricia rightly mentioned)
http://www.northvegr.org/zoega/index002.php?
PHPSESSID=2bc83bc631bdf9aac06c4039ba979f8b
http://norse.net.ru/ondict/zoega/index.html
Icelandic dictionaries of Cleasby & Vigfusson, and Zoega (together
with works on Gothic, Old English, Old Saxon, Old High German, Old
Frisian, etc. at Sean Crist's Indo-European Language Resources)
http://www.ling.upenn.edu/~kurisuto/germanic/language_resources.html
http://www.ling.upenn.edu/~kurisuto/germanic/oi_cleasbyvigfusson_abou
t.html#images
The digitised dictionaries here are still in the process of being
corrected by hand, but if the page you want is too garbled you can
always look at the scanned version. Cleasby & Vigfusson's
dictionary is bigger than Zoega's, so more words and more detail,
and more examples, but also easier to get lost in.
MORE LINKS
http://www.oe.eclipse.co.uk/nom/norselinks.htm