From what I see, you are taking mainly landscape style photos. For this, you want a small aperture setting.
What does this mean? The Aperture is a hole in the lens that controls how much light comes in. The trade off: big hole = more light in, but shallower depth of field (less is in focus). Small hole = less light in, but larger depth of field (more things at different distances are in focus). So for these kinda photos, I would say start playing around with the aperture. Typically, f/16 is recommended for these kind of photos.
However with a smaller aperture, comes longer shutter speeds. Take you hand and hold it out in front of you. Notice it moving? Yep. That is what your body does, moves. As you can imagine, the longer the shutter is open, the more prone your body is to affecting the image (AKA, your hands are shaking and thus, shake the camera, which shakes the image). From personal experience, 1/60 seems to be the lowest I like to go. Now I have gotten good shots at 1/10th shutter speed with a VR lens, but that was a lucky shot.
So how do you combat this? Tripod! A wal-mart tripod works well with a DSLR with the stock lens attached. As long as you don't start using heavy duty BAMF lenses (which I assume you won't) these little tripods work well. Heck, mine that I bought in 05' finally bit the dust on my last shoot. Its been a good one, I feel like I need to give it a proper burial or something. Bottom line, you can get a good-enough tripod for the same as taking your lady out for a fancy dinner sammich and a beer. Yes, I know. SOMETHING ELSE to carry. But I think you will see a difference in your photos if you do these two things.
Keep in mind what I suggested above is for LANDSCAPE photography only. You try to do this for off roading or sports and you will be upset with your results (well, assuming the planets don't align and grant you awesomeness, it has happened before but I wouldn't count on it).