What are the benefits of having a remote shutter release?
The primary use for a remote release, whether they're wired or not, is to prevent camera shake during long exposures. Long exposures will magnify any shake in the camera, especially those created by even careful hands on the shutter release, so a remote is used to eliminate that.
Now, the added bonus of a wireless remote is for the big group shots you're in. You no longer have to run into the group while the timer counts down, you can simply point the remote at the camera and release from a distance assuming, of course, that you can trigger from the front and the back as not all cameras do that.
Anyways, I have both the wired and wireless for my camera and use them, especially the wired, like crazy.
There are several reasons why you might want to.
- To control the camera from a large distance, e.g. when shooting shy wildlife
- To minimise camera shake
- To take self-portraits
- With certain programmable wireless releases, you can set up time-lapse sequences and/or long exposures (longer than 30s) using bulb mode
In addition to the reduction of shake mentioned by @John, they can also be useful for portraiture. For more see another of my answers.