You can do it, but needs to be a semi manual process.
1) Copy everything on the second partition to another physical drive, such as an external hard drive. To be safe, you may want to clone the contents of both partitions to an external drive, also to separate partitions. That way, once you get to the step where you remove the second partition on your main internal drive, you for sure have it backed up. Also in case of a tragic screwup, you can boot to the external and clone things back. Make sure the external drive is bootable by having it partitioned with a GUID partition table. Any or all partitions being Mac OS Extended does not automatically mean you can startup to it if the partition table is not GUID.
Example:
Let's just presume "Snow" is the partition I want to remove and have "Mavericks" take over its space. I would clone all content on drive "Snow" (which will be the drive icon's same name on your desktop) to the external drive. Once the backup is complete, move to the next step.
2) Launch Disk Utility. Highlight the internal drive's physical drive icon, which is indented to the left. Click on the Partition tab (as I did above). Here I would click on the "Snow" partition at the right (in the graphical display, not the left hand list) and click the minus button below it to remove that partition. The space will be displayed as an empty gray area.
3) You can now grab the lower right corner of your remaining partition down to fill the space and have it take over the entire drive. Click Apply.
In the example above, I would drag the corner of "Mavericks" down to fill to the bottom, leaving two partitions. If wanted to, I could remove both "Mavericks" and "Snow" and then drag "Video" down to take over the entire drive.
4) Copy everything back from the external drive you backed up from the now removed partition.