Is there a way to shut down a Nether portal with redstone?

You can put a single bucket of water into a dispenser. When a dispenser "dispenses" an empty bucket, it actually "picks up" a source block in front of it. By putting a single water bucket in a dispenser, when it's activated once it dispenses the water and when it's activated again it removes the water.

You can use this to make a button- or other restone device-triggered "off switch" for a portal. This is a complete reference design:

The trench behind the portal is what keeps the water from flowing everywhere:

To turn it back on, you can build a dispenser with Fire Charges directly against the frame. The Fire Charge goes through the frame, lighting it. The only problem with this is that it consumes a resource that has to be occasionally replenished. Thanks to Resorath for the tip and the video that demonstrates the technique:

I happened to be in need of shutting a portal down from the Nether side.

I built my project in an Overworld test world and when i finally built it i realized i couldn't shut the portal off because i was using a dispenser producing a single tick of water, which unfortunately, doesn't work within the Nether!

I happened to find the simplest of the solutions, that im writing down here just to add to the previous ones. LAVA

By dispensing lava into a open portal, we break it. Nether side fixed. Yeah.

Here is my portal on/off setup, as compact as possible.

This is the front, in the left dispenser i put Flint & Steel, in the right one bucket of water (if Overworld side) or bucket of lava (if Nether side)

Hope is useful!

Minecraft version 1.5 allows flint and steel to be used in a dispenser. When the dispenser is activated it will light the Nether portal.

From the wiki, the only ways to deactivate a nether portal are explosions or pouring a water bucket directly into the portal. If you don't want to have anything explode, it looks like you will not be able to deactivate it with redstone.

One option, if you want to try using TNT without destroying anything nearby, you can use obsidian to direct the blast towards the portal and then just make sure that there is nothing important in that direction.

The answer could evolve with time and updates, but:

As of 1.1.0, with a Vanilla client, no, it's impossible. Plenty of mods will allow that however.