Mac OS X allows you to remove and rearrange the built-in system icons on the menu bar. Icons like Time Machine, Bluetooth, WiFi, Volume, Power, and a few other icons including the date and time (as seen in the orange box in the screenshot below) can be rearranged with ease.
To rearrange the system icons, press and hold the Command key, then click/tap the mouse cursor on the icon and drag it left or right to a new location.
To remove system icons from the menu bar, you need to edit the Preferences of each specific item.
For example, click on the Time Machine icon and choose Open Time Machine Preferences, and you will see a Show Time Machine in menu bar check box.
However, in some cases you need to dig just a little bit. To remove the volume icon, you need to go to System Preferences | Sound and uncheck the box next to Show volume in menu bar. I think at this point you get the idea.
But, how do you rearrange or remove non-system icons in the menu bar that are installed with third-party applications?
Unfortunately, there is no native way in OS X to rearrange third-party application icons in the menu bar. However, each application may or may not offer the ability to toggle its menu bar icon on/off. For example, the icon for CrashPlan (a cloud backup service) allows you to turn off the CrashPlan icon in the menu bar. Simply click the CrashPlan icon, choose Preferences and uncheck the box next to Launch CrashPlan menu bar on login.
You can also right-click/double tap an application icon (although not all applications icons support this) and choose Quit, but that likely will cause the entire application to cease operation, which is not likely the desired outcome.
And in some cases (like Dropbox) you need to browse to another menu (often depicted with a “gear” icon) to find the Preferences and/or Quit options.