Recently I noticed several popular web applications which go for sidebar navigation without labels. E.g. Evernote or Taiga
Is it ok for sidebars? As most users will use those applications several times a week and they get to used to it?
Saying 'a user will get used to it' is really a design excuse: people may not be willing to take the chance of just clicking on your icon to see what happens. Not used these apps, but Google Ventures uses a good technique where the labels for the icons are shown onMouseOver. I'd recommend that as a good way to teach people what your icons mean without the need to display them on the screen all the time.
Like with any icons that don't have labels, it can work really well if all the icons are super transparent. Good all-time examples are Add, Search, Settings, Menu, or Home. As the functionality gets more complicated, usability problems might arise.
Hover captions might help with that, but keep in mind they're not visible on touch devices.
It's up to you whether to use this or not, indeed the user will be able to quickly empirically learn what's hidden behind the icons (the lesser evil).