Stranded Cotton
This is the standard thread used for embroidery, sometimes called embroidery floss. It's made up of 6 strands of cotton, so you can use any amount between 1 and 6 strands - or even more! I always separate out all the strands I'm working with so that they look neater and become easier to work with. 6 stranded floss can also come in variegated colours, metallic and silk. The two brands I recommend are DMC and Anchor. They are good quality threads and have a wide range of colours to choose from.
Perlé
Perlé, or pearl cotton, is another type of cotton thread. It's made of two strands twisted around each other and has a slight sheen to it. Unlike stranded cotton, you do not split the threads of perlé. It comes in a range of different sizes but is generally thicker than embroidery floss. Also made by DMC and Anchor.
Coton a Broder
Coton a broder is similar to perlé in that you do not split the strands and it comes in a variety of sizes. Unlike perle, it has a matte finish. Again, DMC and Anchor are the brands used most often.
Sewing Thread
Regular sewing thread is often polyester rather than cotton, but is still perfect to stitch with. It's a very thin thread so can be great for small details and shading. Gutermann is probably the most common brand.
Wool
There are a couple of types of wool specifically for embroidery, such as crewel wool (2 ply) and tapestry (4 ply). But of course you can also stitch with knitting and crochet yarns. Appletons is the most popular brand for embroidery wools.
Ribbon
Ribbon embroidery is generally done using 100% silk ribbons. They come in a variety of widths - 4mm and 7mm being the most popular. I stock a small amount of silk ribbons in the be alice shop, but for a wider range you can go to Crafty Ribbons.