P.S. If you are working on Windows 10, may be could be of interest this more recent post of mine.

I was testing how the last version of public OneDrive works in Windows 8.1 and I noticed that there is (no more) the feature to synchronize a generic folder other than the OneDrive one. Moreover it is not possible to not synchronize a subdirectory or a file in OneDrive directory, but only that directory as a whole.

So, if I you have the OneDrive folder synchronized, if you delete some file or directory in in, this change will apply also on the remote cloud (so you loose all that locally deleted files). No way to delete some local OneDrive file/subdir (to free HD space, even the one that it is taken with “on-line only” option) and make them remain only in the cloud (and maybe in an external local backup HD)!!
I asked also in the Microsoft forum and their answer confirmed that.

So:

• Only files and folders that are inside the OneDrive folder will be synced to the cloud.
• All the files and folders inside the OneDrive folder will be synced to the cloud (unlike the previous Operating System where you can choose files to sync locally on the computer).
• Files removed or deleted from OneDrive folder will be removed from the cloud. The only option is to set it online-only (smart files), which will not take up space on your computer (e.g. a photo of 6MB, locally will take only 28KB of your local HD space)
  

  Make online-only files (1)

Make online-only files (2)

I hope that in future releases there won’t be these limitations anymore …
It’s really a pity that it is not possible to synchronize also a generic folder and let one OneDrive subfolder not to be synchronized. So, no way to put files only remotely and not have any reference anymore in your local PC (unless you do not synchronize all the OneDrive content).

However you can always change the place where the local OneDrive directory is set, going in the properties of that folder and possibly change it (e.g. to be set in the more convenient partition of your PC or possibly on an external one_).

Locate the local OneDrive dir where you like

See also the following link: Troubleshoot Sync Problems in OneDrive.

If you want to have that feature become available, you can send Microsoft your feedback or feature request through this link: Talk to us about OneDrive (formerly SkyDrive)

PS: I copied a lot of files from my PC (Windows 8.1) to OneDrive (selecting all files in a local directory and then drag&drop in a OneDrive directory in a browser) but at the end (many hours later) I realized that some files weren’t transferred for some reason.
Because it was hard to identify all the files not already transferred, I repeated the copy&past operation sure that there was an option allowing to copy only the not already existing files on OneDrive directory (as it usually happens when you copy some files in windows with file explorer).
However it was asked me only the option to Replace or Keep All pre-existing files: because I hoped that the other choice could avoid the transfer again of all the files I chose that …. however I had all the already previously transferred files duplicated.

If, as in my case, you have to put in OneDrive many photos and for whatever reason something go wrong for the transfer of some of them, it is difficult to find out what are the ones not transferred yet. So, it should be very very useful to have and additional choice to the exiting ones (Replace, Keep all) that allows to copy only the files not already available in the OneDrive directory where you do the drag&drop (Skip the tranfer of all the already present files): therefore, if the file was already available it should not be transferred (saving time and a bandwidth usage). In OneDrive it seems to me that the only way to not transfer anymore already present ones is to click the x icon in every listed file, notified as already present …

This additional option is available for example in windows Explorer, when you copy&past from one directory to another, so I think people expect this useful feature to be also available in OneDrive.
Note that I used the OneDrive Web (OneDrive.live.com) and not the the OneDrive local directory, actually not synchronized in order to avoid wasting of local memory space on my PC.

what it happens with a drag&drop in Windows Explorer is that if some of the files are already present on the dragging directory, you can choose to skip the tranfer of all of them at once.

In the drag%drop in OneDrive I think that this is not possible and whatever you choose Replace or Keep All the transfer of that already present file is done (in one case it is replaced and in the other case you will have two copy of each file).

If you want not to transfer only the already present files you are not asked (as it happens in Windows Explorer) if you want to skip one file transfer of all of them if they are already available in the dropping directory. You have to click the x icon in every listed file, notified as already present, to have it not tranferred …

===========================

I also tried OneDrive for business and in the following I put some considerations.

Also for this version there is both a web client, with drag&drop function, and a app client. It is strange that in Windows 8.1 there are two different apps, one for OneDrive and the other for OneDrive for business, while in Windows Phone there is only one app that works for both environments (from a upper left menu, you can simply switch from one to the other).

Moreover in OneDrive for business the maximum number of files you can drag&drop is only 100 instead of the 1000 of the public OneDrive.

An other (great) limitation I experimented in OneDrive for Business is that it doesn’t allow to have an thumbnail preview of some type of files like .jpg ones … and this is very bad for pictures!!

I also wrote a post in the Microsoft community forum asking for clarifications and they confirm my feeling: I want to stress the efficiency of that forum … I received an answer after few hours on Saturday!

A colleague of mine also point out other limitations: one related to the transfer of files with some extensions (e.g. json) and an other related to the length of the file name (even if are names chosen by the Windows OS).