Tiny sharp points
I can't live without scissors that snip cleanly into a tiny tight spot. My favorite brand is Kai, but I do have several others that I've used over the years. The points should be so tiny and sharp that you literally stab yourself from time to time. (Not on purpose). I like that these scissors come with a little sheath and a cord to hang around your neck.
Spring loaded thread clippers.
I have 2 pairs of these from Fiskars. One is so worn out, I probably need to replace it. These are a wonderful pair to clip threads at the sewing machine, or anywhere else when you cut a lot of thread. The spring loaded feature means that you exercise your hand less since you don't have to open the scissors first. I believe these come in several sizes, but this is the size I like to use. They fit into all of my traveling sewing kits.
Large handles, small blades
I was first introduced to this style by Sharon Schamber. They are great when you have to do a lot of tedious trimming (think applique). Since most small scissors also have tiny handles, this style really helps your hand from getting tired. Much more ergonomic. The pair on the right are from Karen Kay Buckley. They are micro-serrated and super sharp.
Large blades and large handles
We probably all have one of these styles. I have several including the classic Gingher from my garment sewing days, one from Kai because they are so comfortable, and an old Fiskars pair, mostly for cutting interfacing, dissolving products and paper patterns.
Blunt edge, applique
If you do any trapunto or like to cut away the background from an applique pieces these are very handy. The blunt (or rounded) edge won't stick into your fabric and slides nicely right up to the edges. I'm sure there is a proper name for this type, but I can't think of it right now.
Serrated edge for applique
A relatively new introduction to me are the tiny serrated edged scissors They hold the edge of the fabric as you cut out your applique pieces and are very useful on tiny pieces or pieces on the bias. I love the little green ones shown above from Karen Kay Buckley. People who do more sewing than quilting would probably like the larger styles.
Medium sizes for clipping corners and small pieces
I have several different sizes in the medium range, and I like all of the Kai scissors for their different lengths and comfortable handles. I also like Fiskars.
These are so great for sewing garments and home dec. I don't use them that much in quilting, but I know several people who pink the edges of their fabric before they pre-wash it. Nice to have when you need them.
I reserve two pairs for paper cutting and use these when I do pattern work, for cutting fusible release papers, and for whenever it feels like I'm cutting something that will dull my scissors. These are my more inexpensive scissors, and I don't mind if anyone in the house grabs them for cutting something.
I hope you check out the scissors at your local quilt store, your local fabric store, and the manufacturer's booths at regional quilt shows. You never know when you'll see that new perfect pair of scissors. Happy cutting!