So, I have been analyzing the crash reports that I sent to the Opera development team and Ubuntu Launchpad. The reason why Opera crashes so frequently on my system is due to the high number of open tabs that I keep using (i.e., 10+ open tabs). I also have to wait for the next update to the Opera browser in hopes that the software engineers will address this issue.
When I use Opera 10.60 on my Windows XP Home Edition SP-3 partition, it runs stable with no crashes regardless of how many open tabs I have running. I have experienced no crashes so far.
I find it interesting to see how difficult it is to code the same application on multiple operating system platforms with very different results.
There is nothing more that I can do other than to wait patiently for an update that patches this problem and keep the number of open tabs to a minimum.