This is an ongoing issue, some customers reporting they don't have the Browse option in the desktop client. Browse being missing has been solved for quite a few people, however there are still reports of this issue.
Anyone with an affected account will not have the Browse option, which is at the very top of the left hand panel in the Desktop client.
Searching for: "spotify:app:browse" is reported to work for the majority of people experiencing this issue.
In order to help track down this issue, please provide the details in the section below.
If you are having this issue, can you please post:
Your desktop operating system (Windows 7/Mac OS X 10.9.x etc).
Your desktop spotify version (Help/Spotify > About)