I use the following construction:
MyObject obj = new MyObject();
obj.setSomething("something");

Then:
Session sess = HibernateUtil.currentSession();
sess.save(test);
sess.flush();

but the above code works only once, then table is empty. my object receives id=0;
then this code is invoked in second time - i receive exception:

12:25:22,968 WARN JDBCExceptionReporter:38 - SQL Error: 1062, SQLState: S1009
12:25:22,968 ERROR JDBCExceptionReporter:46 - Invalid argument value, message from server: "Duplicate entry '0' for key 1"
12:25:22,984 WARN JDBCExceptionReporter:38 - SQL Error: 1062, SQLState: S1009
12:25:22,984 ERROR JDBCExceptionReporter:46 - Invalid argument value, message f
rom server: "Duplicate entry '0' for key 1"
12:25:23,000 ERROR JDBCExceptionReporter:38 - could not insert: [com.overalltest
ing.hibernate.objects.Test]
java.sql.SQLException: Invalid argument value, message from server: "Duplicate
entry '0' for key 1"
at com.mysql.jdbc.MysqlIO.checkErrorPacket(MysqlIO.java:1697)
at com.mysql.jdbc.MysqlIO.sendCommand(MysqlIO.java:1083)
at com.mysql.jdbc.MysqlIO.sqlQueryDirect(MysqlIO.java:1142)
at com.mysql.jdbc.Connection.execSQL(Connection.java:1876)
at com.mysql.jdbc.PreparedStatement.executeInternal(PreparedStatement.ja
va:1590)
at com.mysql.jdbc.PreparedStatement.executeUpdate(PreparedStatement.java
:1653)
at com.mysql.jdbc.PreparedStatement.executeUpdate(PreparedStatement.java
:1492)
at net.sf.hibernate.persister.EntityPersister.insert(EntityPersister.jav
a:502)
at net.sf.hibernate.persister.EntityPersister.insert(EntityPersister.jav
a:433)
at net.sf.hibernate.impl.SessionImpl.doSave(SessionImpl.java:876)
at net.sf.hibernate.impl.SessionImpl.doSave(SessionImpl.java:817)
at net.sf.hibernate.impl.SessionImpl.saveWithGeneratedIdentifier(Session
Impl.java:737)
at net.sf.hibernate.impl.SessionImpl.save(SessionImpl.java:717)
at com.overalltesting.servlets.TestDetailsParser.doPost(Unknown Source)
at javax.servlet.http.HttpServlet.service(HttpServlet.java:165)
at javax.servlet.http.HttpServlet.service(HttpServlet.java:103)
at com.caucho.server.http.FilterChainServlet.doFilter(FilterChainServlet
.java:96)
at com.caucho.server.http.Invocation.service(Invocation.java:315)
at com.caucho.server.http.HttpRequest.handleRequest(HttpRequest.java:246
)
at com.caucho.server.http.HttpRequest.handleConnection(HttpRequest.java:
164)
at com.caucho.server.TcpConnection.run(TcpConnection.java:139)
at java.lang.Thread.run(Thread.java:534)

WHAT IS THE PROBLEM ?

in hbm.xml i have:
<class name="com.overalltesting.hibernate.objects.MyObject" table="MY_TABLE">
<id name="id" type="int" column="ID" unsaved-value="0">
<generator class="identity"/>
</id>
<property name="something" type="string">
<column name="SOMETHING" sql-type="TEXT" not-null="true"/>
</property>

Are you sure your field is of type AUTO_INCREMENT in your database ?

Hint:
try to remove the unsaved-value directive in your mapping config... God feeling ;-)

Damn, is it should be AUTO_INCREMENT ? I thought incremention is Hibernate's job :(

Nope - the INCREMENT generator uses the database facilities...
If you want Hibernate to generate the ids itself, use another generator like HiLo, Increment, etc.

Done, it's working now... thanks a lot !