I think the people saying "none" are pretty much dead-on. Just for example, consider portable devices using things like Windows CE. They use battery-backed RAM instead of memristors (or competitors like FE-RAM), but the basic idea is the same: your primary memory is (effectively) non-volatile. Despite this, nearly all such devices divide the memory into two sections, one used as main memory, and the other for file-system storage.
In theory there's no real need for that. They could, for example, do like MULTICS did, and map it all as virtual memory, with the possibility of giving names to memory regions so you can treat them (somewhat) like files. For that matter, given the address space of a current CPU, you could go even further: you could map the entire Internet as a giant address space, so retrieving a page from site X would be treated as simply paging in some virtual memory.
I can think of at least two reasons that hasn't happened, and shouldn't be expected to happen any time soon either. First, it doesn't fit well with the way most existing software works. You'd have to throw out nearly all existing software (applications and operating systems) and start over from the beginning to really take advantage of this.
Second, it doesn't seem to fit well with the same most people think and work. I could think of all the data on all the servers in the world as "virtual memory" for my computer, but most people don't. From an electrical viewpoint, there's not even all that big of a difference between a SATA connection and (say) an Ethernet connection. While things like storage area networks and iSCSI have helped erode many people's perceptions a little, most people still think of "memory", "files", "local", "remote", etc., as being quite distinct from each other.
These don't remove (or even substantially reduce) the need for things like serialization either. Yes, while I'm working on a file on my machine, it wouldn't have to be serialized -- but the minute I decide to send the file to somebody else on their machine, I need a way to serialize ("marshall", if you prefer) the data so they can use it on their machine. The capability might not be used quite as often, but it would still need to be present.
Likewise, you'd need some way to back up, restore and (by strong preference) version your data. This (again) generally requires some sort of serialization, so I can take a "snapshot" of the data at some point in time and have it coherent so I can use it later. That might not be exactly the same as serialization the way most people think of it right now, but offhand it seems like it would be reasonably similar.
Bottom line: In theory it might be able to change a lot in a hurry, but in fact the net effect is probably to make it easier to (for example) produce portable devices that work almost exactly the way they do now, but get longer battery lives because the RAM will draw power only for reading/writing, not just to maintain its current contents.