Animated GIF of recorded screen activity
ScreenToGif is a free app for Windows to record directly to an animated GIF.
You simply have to position the transparent window above the content you wish to record and then it provides the necessary tools to remove frames, adjust the animation speed and add overlays.
NOTE : As pointed out by @richard's comment, this answer is outdated. 'All-in-one' alternatives in other answer and comment below.
There is no free "All-in-one solution" for screen recording in gif. You can use any screen recorder to capture in video format and then use some tools to convert video file to gif.
One possible solution:
Use CamStudio Portable to record your screen activities to AVI.
Use VirtualDubMod to convert the AVI to a sequence of images (PNG).
Use Easy Graphic Converter to convert the PNGs to GIFs.
Use UnFREEz to create an animated GIF from the images.
Source: Screen recording in animated .gif format.