I know that is probably the most common phrase. If someone tells you something that you already know, you could respond "I know" or "I know that but ...". In general, "that" is for something else, further away (in this case, whatever the person is telling you about).
"I know this" sounds like something you would say to yourself when you realized that you remembered something about it before -- like if you thought that you didn't understand something and then realized that you did. In general, "this" is for things that are nearby -- in this case, the thing in front of you that you're realizing that you understand.
"I know it" sounds like something you'd say if you were expressing confidence in something. Like "I just know that they're going to be late" or "I just knew that there would be problems with the flight".