Preamble :
Imagine that when viewing a video that is very important to you, you discover that you did not see the big "http://declic-video-fx.com" was stuck on the lens of your camera. It looked something like this :
Oh darn ! 
Don't panic, we have the solution.
This tutorial will show you that by using VirtualDub and the DeLogo filter from Karel Suhajda you can remedy this unfortunate situation.
Step 1 : Softwares installation
You may refer to Step 1 of our tutorial Video Transcoding with VirtualDub. The only difference is that there will be no need to create the plugins32 directory. On our download page you can get the delogo121.zip file. Extract the .ZIP file and copy/paste its contents in the VirtualDub plugins directory.
Let's start VirtualDub by selecting VirtualDub.exe or launching its shortcut from the desktop. In the Menu File we load our video with Open video file...

Step 2 : Filter application
Apply the DeLogo filter by going to Video Menu and select Filters ... :

Then, Add... and select the filter DeLogo1.2.1 by pressing OK :

The filter settings window opens automatically. That is what you'll see :

Step 3 : Filter Settings
Click on Show preview and in the window that opens, with the scrubber, choose a passage where the logo is clearly visible. In my case it is at the end of the video where the logo appears on the clear blue sky.
Return to the filter and select Save frame :

The recording format must be BMP.
The BMP must be opened with an image editor like Paint. With a brush type tool you must fully cover the logo with a pure red (255,0,0).
Don't be afraid to go outside the logo a little and be sure all the pixels inside the logo are colored red.
This is the result :

In fact, we have just created a mask. It is on this mask that we will apply the blur algorithm filter.
Return to DeLogo and load this BMP file with Load... in the Repair section :

With Show preview you can see the results right away. If bits of the logo are still showing, you will have to add red to BMP, then save it again, reload with Load... all this without leaving DeLogo.
Step 5 : Last settings
In the Repair parameters zone :

you can fine-tune your work by modifying the following parameters :
- Specify whether the video is interlaced or not with the Interlaced check box.
- Increase or decrease the impact of the blur applied to the red mask by changing the Depth. It determines how many pixels wide around the red will be blurred.
- With Power you can set the blur intensity.
- Finally, with Pixel aspect you can modify the PAR (Pixel Aspect Ratio) depending on the format of the original video 4:3 or 16:9.
You can view the affects of your changes in real-time thanks to Show preview.
Step 5 : Export result
When you're done, click Close.
Then I invite you to read Steps 3 through 6 of our tutorial Video Transcoding with VirtualDub.
If you've done it correctly, the final result should be close to this:
It's magic, isn't it ? 
{Thanks to Loosecannon for the fine tuning}