Are there any advantages to partitioning a SSD on a Mac? I have a Macbook Air with 128GB SSD. It's used to be a best practice to put the OS on a separate partition from data.

Does that make any sense? What are the advantages to partitioning an SSD?
There are no compelling advantages to partitioning the main SSD/HDD for a single OS install under OS X. 

Regardless of SSD vs. HDD, it really only makes sense if you need to re-install your OS frequently (which you shouldn't need to do with OS X), and want to be able to keep your data around while wiping your OS partition. There's no performance benefit to be had, and it requires more tinkering to get things set up (symlinking User directories, etc.).

One of the reasons to partition in the past was to improve speeds for some files by taking advantage of the physical location of the data (transfer speeds are higher on the outside of a disk platter). With SSDs, physical location doesn't have an effect on performance, and modern OSes can optimize for best disk performance on HDDs automatically, so there is not much gain to be had from micro managing storage allocation as in the past.

Unless you have a very specific reason for not doing so, just use one partition and enjoy your Mac.