All Oracle products require a license to be purchased for use, unless this is meant for personal learning purposes. The license agreement is here - http://www.oracle.com/technetwork/licenses/standard-license-152015.html - you need to read and accept the terms before you can download the software.
As Srini said, the Database Gateway for Sybase (DG4Sybase) requires a license.
The only way you could connect to Sybase for free is to use the Database Gateway for ODBC (DG4ODBC) but this needs a third party ODBC driver. If you can find a free ODBC driver that fits the criteria in the documentation then it would be free for you. The license for DG4ODBC is included in your RDBMS license.
You can find further information, details and links to the certification matrix in this note available in My Oracle Support -
Thank you for your response. One last related question -- do you know of any performance issues with using the Oracle Transparent Gateway for Sybase? We need to keep the two databases in-sync as close to real time as possible...
All the gateway does is send SQL to the remote database so there can be network delays sending the data back to Oracle.
However, the main performance problem with any gateway is when data needs to be post-processed. This means all the data from a remote select needs to be returned to the Oracle database to be processed when you use syntax or functions and such like which cannot be processed on the remote side.
The following note available in My Oracle Supprot discusses this further -