<p>We're a .NET team which uses the Oracle DB for a lot of reasons that I won't get into. But deployment has been a bitch. We are manually keeping track of all the changes to the schema in each version, by keeping a record of all the scripts that we run during development. </p>

<p>Now, if a developer forgets to check-in his script to the source control after he ran it - which is not that rare - at the end of the iteration we get a great big headache.</p>

<p>I hear that SQL Compare by Red-Gate might solve these kind of issues, but it only has SQL Server support. Anybody knows of a similar tool for Oracle? I've been unable to find one.</p>

TOAD is a great generic tool for Oracle development and i think a similar feature is in the basic version. You can download a trial version (make sure you don't get the old free version of TOAD, that is about 4 years old)
If you don't want to buy a tool, and you need something less flash you could roll your own quite easily. I just found
Schema Compare Tool for Oracle
which looks very simple, and has a nice baseline concept. This is very handy if you want to track changes since the last code check-in. This way you discover changes that may have been made to multiple DBs by hand, but not documented.
PS: The "SQL Compare by Red-Gate" demo looked very nice indeed... however the voice over cracked me up... sounded like a BBC documentary.