What are the available options to backup DB2 Express-C? I want to use DB2 Express-C edition with my application. I have never used DB2 but now want to use the Express Edition in a production environment to learn more about it.

I want to know what are the various backup options available in the Express Edition. In case of a sudden Windows DB2 service failure, how to recover data files?

Is there a way to just copy data files from one PC and attach on another instance of DB2 running on another PC?
Well, DB2 has a backup/restore system, and this allows to make full, incremental and delta backups. For more information about this, you can take a look at: http://publib.boulder.ibm.com/infocenter/db2luw/v9r7/topic/com.ibm.db2.luw.admin.ha.doc/doc/c0005945.html

However, if you want to do a clone of the database, by just copying the data files, you could use the split mirror feature. This feature will stop all IO writes to the database, and you just have to copy the tablespaces and database files into other disk and voila.
For more information about spli mirroring: http://publib.boulder.ibm.com/infocenter/db2luw/v9r7/topic/com.ibm.db2.luw.admin.ha.doc/doc/t0006422.html
This feature uses the "set write"command: http://publib.boulder.ibm.com/infocenter/db2luw/v9r7/topic/com.ibm.db2.luw.admin.cmd.doc/doc/r0009503.html

Other recent features in DB2 includes the possibility to merge backups, restore tables, and more characteristics that are part of the DB2 recovery expert: http://www-01.ibm.com/software/sw-library/en_US/detail/W269469I30015Y81.html