Throughout the year I try to get to know the teacher a little bit... what they like, what their interests are. Some teachers are very open and it's easy to do this with, others are more reserved or private and it's more difficult to know. But, generally, you can find at least one or two things that make them smile.
A few years ago, our oldest son had a teacher who was really into making things from scratch. It didn't matter if it was cooking or art or even building his home or car... he liked to start from the ground and work up with just about anything he did. So we made him homemade beeswax candles, and also set him up a kit with instructions so that he could learn to make them, too. The next year when we saw him at school again he said he'd made several batches of his own candles, and thanked us for the great gift!
One year we had a lady teacher who loved fuschia's - a very pretty flower that does well in hanging baskets. So we gave her some of those with a handwritten note and she loved them. Some gifts are as simple as that.

She was one of those teacher's whom we never really knew. She was very reserved and private. But we managed to find out about the flowers at least.
This year, our teacher loves the coast, nature, the outdoors, gardening... she's very natural and earthy and very big into recycling and the environment. So we've been collecting driftwood pieces during our visits to the coast and my son is making her a special driftwood mobile to hang in her garden or around her house. He's drilling holes in each piece of driftwood and then stringing the pieces together with a sturdy cord. He's thinking of using mod podge and recycled bottle caps to include a picture of him as well... (cutting out a picture of his face, gluing it inside the bottlecap, then mod podging it to seal it) and hanging that at the end of the mobile, to remember him by. He's also added some pretty beads between the driftwood pieces that will catch the sunlight and sparkle.
We've also done gift baskets... just a basket full of fruits, teas, baked goodies, yummy stuff... that's a good thing to do if you don't know the teacher very well.
One year we had a teacher who was crazy about coffee... and we knew the coffee shop that she went to every morning on her way to school... so we bought her a gift card for that shop. We gave her enough so that she had free coffee for a month!
Having your child write a nice letter is always a good idea. We did a sweet poem many years ago... we did a line for each month of the school year, September through June. I actually wrote most of the poem, but then my son copied it in his handwriting. I think he was like 7 or 8 that year. The teacher loved it.
I saw at Walmart the other day these kits where you can personalize canvas bags. They have these iron-on patches and things, and lettering. Maybe your teacher would appreciate a nice bag to carry things in? It seems teachers always have so much to tote around and keep organized!
This is a fun time of year... good luck with your gifting adventures!