Big, double-thickness flannel baby blankets are easy and always appreciated. When you buy the flannel measure how wide the fabric is (it says on the end of the bolt, or ask the person at the cutting table), add a few inches (because the cutters never cut straight) and that's how much you'll need. Do the same for a coordinating fabric (for the back). Cut them straight and cut off the selvages, then stitch around all four sides, leaving the last 6 inches open for turning. Trim the corners so they're not bulky, then turn inside out and iron flat. Fold the edges of the opening in and iron them flat. Pin around it, then top stitch around the edge of the blanket. If your sewing machine has cute stitches, this is the time to use them! My mom's sewing machine could stitch letters, and she sewed "sweet dreams little one" all around the edge of a blanket for my baby. If you wait until you have a name, you could do that.
Then you should stitch a big square in the middle of the blanket to keep it all together. Did that make sense? You can do a cute stitch for that, too.
It seems to me that one of those organizers that you hang over the back of your car seat would be pretty easy to stitch up. They have patterns for lots of this stuff at WalMart.
I made a bunch of knit hats for my babies. I bought a cheap one for like a quarter at a thrift store, picked it apart, and used that as a pattern. Then I made them cute. Like on a green one, I appliqued eyeballs and a mouth and it was a cute frog hat. I had knit the color of Pooh, so I made one with ears and stitched a Pooh face on it.
I found this blog with ideas and free patterns:
http://www.sewmamasew.com/blog2/?p=233
I hated those flannel burp cloths. They're cute but my boys spit up way, way too much volume. But you could do some decorative stitching around some cloth diapers (my favorite burp cloths), or sew ribbons onto it (my sister did that and it was cute).