Hopefully the answer to this doesn't turn into a slug fest.
(First post is from the SQL Server point of view, hopefully one of the Oracle guys will post as well.)
SQL Server using T/SQL language, Oracle uses PL/SQL
SQL Server can only be installed on Windows - Oracle can be installed on several OSs included Unix, Linux and Windows
Oracle's licensing system is much more complex than SQL Servers.
Oracle's CPU licenses are done per CPU Core, SQL Servers are done per physical CPU.
Both products are very good database platforms and when run on similar hardware will usually give similar performance.
Typically deciding which one to use comes down to a personal preference, and what product you have prior experience with.
In general, I agree with Mrdenny, and I think the most important difference is the one related to the supported Operating Systems.
There are many internal differences, such as the way concurrency is managed, the types of indexes that can be created, maximum length for table and column names, etc, but in general, I also think that both products are very good.
Having worked mainly with Oracle, I have the impression that PL/SQL is more powerful than T/SQL, but that is just my opinion.
Being SQL Server a Microsoft product, I think the integration with the operating system is an advantage of SQL Server, and I also think that it has easier administration, although Oracle has improved this point with the last versions.
Oracle is more expensive...