Blurry/sharpness could be from a lot of things.
Shutter speed
The cat looks like it was shot in low light, so the camera uses a longer shutter time to capture more light. If the shutter is open for a long time, generally > 1/focal length, the camera may move, causing blur. The image stabilizer helps, but it becomes harder with longer focal lengths. Like Z said, you can use a tripod, but this will not help if the subject moves. Well, depending on the shot, you could use the flash to add some light, but that is going to be a different story altogether.
ISO sensitivity
You can amplify the sensitivity of the sensor to light by increasing the ISO, which will in turn allow you to use a faster shutter speed to prevent blur. SLR camera sensors are better at high ISO than compact cameras, but you can still see that you get to an ISO level where the quality degrades by having red, green and blue specks called chroma noise. If you shoot in RAW, you can use software like DPP or Photoshop to remove the noise, but they only work so well. (Also forgot to mention earlier that if you shoot in RAW, you can adjust white balance in software after shooting).
Aperture
Lenses like the f1.8 and f2.8 ones mentioned earlier let in more light which also in turn allows you to use faster shutter speeds to prevent blur. However the side effect is, at large apertures (smaller f number) the depth of field becomes narrower, and you have to be careful where the camera focuses, especially with a Canon XSi which only focuses on the 9 boxes in your viewfinder. In your pics, you can already see a narrow depth of field where the subject is in-focus while the background is out of focus. Actually most of the time a narrow depth of field is used for artistic effect. And don't worry, you can still make the aperture smaller on your lens; the number is just the maximum aperture.
Lastly, if you want to get really picky, the sharpness of a lens changes depending on the aperture, particularly in the corners and along the sides (this is independent of the depth of field). The technique called "stopping down" is where you choose a smaller aperture, and most lenses are sharpest between f5.6-f11. However, smaller than that and sharpness actually decreases.