This the stitch panel on my sewing machine. There are 40 stitches, some of which are purely decorative.
00: This stitch is the moveable straight stitch, meaning by altering the "stitch width" on your sewing machine, you can move the needle. It's default needle position is the far left. This is the stitch you will use the most often for just about everything.
01: This is the centerised straight stitch. It is like a safety straight stitch for sewing zips so that you don't hit the zipper foot. It cannot be moved.
02: This is the Triple Straight Stitch, also called the backstitch, stretch stitch, triple stretch stitch, and probably some other names as well. It made by the needle going two stitches forward and one stitch back. This makes a stronger seam which some people like to use for crutch seams and armscyes. It is also great for sewing stretch fabrics because it doesn't snap like an ordinary straight stitch can (when stretched). You can use it for top-stitching as well if you like.
03: This is the stretch stitch and is also called a lightning stitch. It's a very narrow zigzag. It's supposed to give stretch seams that can be pressed open, but I much prefer stitch 02 for that. I'm not a big fan of this stitch.
04: Ah the zigzag stitch. Stitch of a myriad uses. Neatening raw edges is the most common use. Satin Stitching (length 0.2-0.3mm). Appliqué. Stretch sewing (length normal, width 0.2 or so). Bar-tacks. Very manual buttonholes (if you have an automatic buttonhole, do use it). Satin Stitch in free motion stitching (great for monograms). You can probably add some more uses.
05: The triple zigzag stitch, this has several names as well, but as long as you can see what it is, you'll be fine. Its primary uses are neatening raw edges (especially fabrics that fray badly) and sewing elastic. But as each step counts as a stitch, you can make really long zig zags.
06: Overcasting stitch. This can be used for seaming knits, neatening edges, and making picot edges and shell-tucks.
07: Strong overlocking stitch. Like its friends, this has many names and I don't know them all (who could?) It's used for seaming and neatening at the same time.
08: Same as 07 but it looks different, and the straight stitches are more reliably close together.
09: Blind-hem stitch. It don't think you'll find a machine less than 50 years old without this stitch. Its use is blind-hemming.
10: Stretch Blind-hem stitch. Same as 09 but for stretch fabrics.
11: Appliqué stitch/Blanket Stitch. This is used to sew appliqués and replicate a hand-sewn blanket stitch. It really looks very nice.
12: Shell-tuck stitch. Used with the satin-stitch foot, this makes even nicer shell-tucks than stitch 06.
13: Scallop Stitch. This is used to make decorative edges. First you stablize the edge (preferably hemmed) and then you cut very carefully round the outer edge of the scallop. I suppose if you wanted, you could sew it with the pointed edge towards the edge, and have a pointy edge like a batswing.
14: Ladder stitch: This is used to make channels for elastic and ribbon.
15: Overlocking stitch: This is made to look like an overlocker/serger stitch. It is used for seams, but you can also use it to make channels as with 14.
16: This stitch is for sewing on elastic, like 05. You can also use it for faggoting.
17: This stitch is also used for faggoting, and decorative stitching.
18: Much like 17.
19: This is used for sewing channels too.
20: RicRac stitch. Also ambiguously called triple zigzag stitch. It looks much nicer when sewing than the picture would lead you to believe. It is used for decorative stitching.
21: Serpentine Stitch. Used for decorative stitching and also for attaching elastic.
22: Hemstitch. This is used for doing drawn thread work by machine.
23: Daisy-chain stitch. Pretty decorative stitch. If you carefully poke a bodkin or awl through the middle you can use the flowers as a tiny eyelet.
24: Hemstitch. Yes there are a few stitches called hemstitch. They are used for drawn-thread work by machine. It can look very pretty and vintage.
25: Round-ended buttonhole. Used for blouses and such dainty things. It think if you widen it you could use it on jeans, especially if you use a double thread in the needle (but don't use topstitching thread).
26: Standard buttonhole. Used for anything you want.
27 and 28: Stretch buttonholes. If you are making buttonholes on sweater knits you must interface well top and bottom. I think 28 is best for sweater knits.
29: Keyhole buttonhole: Popular for jackets.
30: Bartack. Made with the buttonhole foot. I prefer to used a satin stitch because it is more reliable.
31: Hand-look stitch. If you use invisible thread in the needle and really increase the thread tension, you can make a stitch that looks like a hand-sewn running stitch.
32-40: The rest of my stitches are decorative stitches. IT is always a good idea to stablize when sewing fancy decorative stitches like these.
35 is called a domino stitch.
36 and 37 can be used like 13 to make very pretty edges.
They are all the stitches on my sewing machine and their primary uses. You can make other uses, because, after all, sewing is a creative hobby.