So you have upgraded to Outlook 2010 and all of a sudden you have become the top speller in the world. At least by Outlook standard, no more wavy red lines are indicating spelling errors.
Well it is unlikely that you became a grade A speller overnight so it is most likely a setting that is turned off by default in Outlook 2010.
To confirm you weren't granted some great spelling powers overnight following the instructions below:
Go to File/Options/Mail, Always check spelling before sending is selected.
Check to see if "When correcting spelling in Outlook" is not grayed out. If it is you most likely have an older version of Office and only the recent version of Outlook.
Some of the spelling options are available only when you have the same version of Word installed. If spell check on send works, the spellchecker itself is working.