<p>What are the other ways of achieving auto-increment in oracle other than use of triggers?</p>

You can create and use oracle sequences. The syntax and details are at
http://www.techonthenet.com/oracle/sequences.php
Also read the article
http://rnyb2.blogspot.com/2006/02/potential-pitfall-with-oracle-sequence.html
to understand the limitations with respect to AUTONUMBER in other RDBMS