I updated a table in my SQL Server 2008 by accident, I was updating a table from another by copying cell by cell, but I have overwritten the original table. Is there a way that I can restore my table contents as it was?
No. If you commited the transaction, the only way to restore the original table is by getting it from your latest backup.
if you have only a backup then restore that to another database and move just the table over (this way no other tables will be affected). If you have also transaction log backups then you can also do a point in time restore
I've heard that there are some tools that might be able to undo certain actions in certain circumstances. Here's a link to an interesting article about how to minimize data loss in these circumstances and it includes links to some tools.
You might want to ask this question at ServerFault as well as some sysadmins might know better.
This tool says it can do it, a bit pricey though. There is a trial period, maybe that will be long enough to get your data back: