There are plenty of souvenir shops all over Sevilla, but you might find that you'll find the best bargains at the major department store, El Corte Ingles, so I would check there first.
If you want details on specific shops, check www.sol.com and look under shopping.
The owner of this shop (I think his name is Guillermo??) designs all of the tee shirts himself so it's interesting to see his art. I bought a couple tee shirts for gifts and they are better quality than the norm. Many times when I buy cheaper shirts they shrink the first time I put them in the dryer, but these shirts are great.
What to buy: I bought a baby shirt for my 8 month old nephew that was pretty cool.
What to pay: Around 10 Euros for children's shirts and 12 Euros for adults.
There are many shops that sell the Spanish fan. They come in all shapes and sizes and can cost from $1 to thousands.
Shop around and find one that you like.
If it is summer I recommend getting a $1 one just for use while you are here.
What to buy: Fans and silk scarfs
What to pay: $1 to thousands of dollars.
There are many shops that sell plates and ceramics. There are very good quality plates to be found here in town but be careful of the stuff made in China.
What to buy: The local ceramics and tile framed mirrors are very nice and can be shiped to your home at a small extra charge.
What to pay: Always try to haggle with the price. Some shops will tell you that their prices are fixed so you should not try with them.
I went to Billabong, and a bunch of other local stores. This was a good city to go shopping in. Lot's of options.
What to buy: I bought a Jacket at Billabong.
What to pay: 80-100 €