Can I remove pagefile.sys to save space on my SSD?

PageFile.sys is your "virtual memory" or "swap space". It is where things from your RAM go when they are not currently being used. You should never delete that file. You may, with some caution, change the Windows system settings that dictate the size of that file, however you are likely to see performance degradation if you do so.

Running without a page file is a very bad idea. If your system is stable, and you don't want to have your pagefile on your SSD, you can manually set its location to another drive - rightclick on "My Computer" (or "this pc" on windows 8.1) "advanced" -> "performance" -> "advanced"

Set no paging file for c: and set it to system managed on another drive. However, if your system crashes, you will not be able to have mini dumps. In that case, just turn it back on while you troubleshoot

If you really want to delete it, first disable it. You can do this from advanced performance options in System Properties.

You can get there by running sysdm.cpl, clicking the Adanced tab and clicking the Settings... button for Performance. Then clicking the Advanced tab in the new Performance Options window and clicking the Change... button.

• Uncheck Automatically manage paging file size for all drives
• Set all drives to No paging file
• Click OK until Windows suggests restarting

After restarting you can safely delete pagefile.sys.

However, I don't think you should ever disable the pagefile, especially if you have an SSD; as an SSD will only speed it up.

Windows always uses virtual memory, and although RAM pools are large enough these days for most people to avoid problems, there's no real benefit in making Windows unstable by limiting that space to the size of your RAM rather than the size of what Windows may need.