ShareX: https://getsharex.com/this looks good
side note how do u add those soundless videos
and
GfyCat: http://gfycat.com/
Basically, I have shareX set up so that when I press Shift-Printscreen, I drag a rectangle for the capture region, Move around in Terraria, click the stop button when done, and a few seconds later the url is automatically copied to my clipboard. I then post it using the Media button that is right next to the Image button, you can just paste the gfycat url there.
More Info: Make sure ShareX has ffmpeg installed (task settings, Capture/Screen Recorder, screen recording options, download), make sure gfycat is chosen as the file upload destination. Gfycat has a 15 second limit, but it is natively supported by the forums, so i use it.