Cotton floss - By far the most common choice for embroidery is the ubiquitous 6-strand cotton embroidery floss. Many people state that they choose it because it looks like silk. It doesn't. Nor does it work like silk. It is, however, much more economical and available in a wider range of colors. I'm not saying don't use it - I'm saying be aware of what it is, what it can do, and what it can't. No mercerized cotton in the world will replicated the sheen and drape of real silk. It also fades more quickly if exposed to sunlight. But for large projects or those requiring lots of colors, it's a reasonable substitute. Keep in mind that the deeper colors have been known to bleed. It sometimes can help to soak them in vinegar water and rinse them thoroughly before use.
Wool - The premier choice for outerwear, as well as many early period projects. It also can be stunning in later period pieces. Wool is a "fuzzy" fiber. It responds best when worked in short lengths. Dyes on wool tend to be more color fast than on cotton. There are a number of good sources for wool embroidery threads, both in modern dyes and in natural. Try to get a sample before you order everything you need for your project since weights vary significantly.
Linen - Linen thread can be difficult to work, as it tends to be quite stiff. It also takes dye less readily and comes in a limited palette commercially. It is phenomenal, however, in heavy wear applications like "prick-stitched" hems. It's also a subtle thread that wears beautifully over time, picking up a softness and sheen with each washing.
Silk - silk embroidery thread is available in both stranded floss and perle weights. Sewing thread is also a good choice for finer works. Brands vary widely in their color palettes, but both chemical and natural dyed silks are available. This is the top-notch choice for Opus Anglicanum and Or Nue. Eterna can be had for $1.00/skein. So it isn't so cost-prohibitive as many people think. Work in short length to prevent your thread from "blooming" with fuzz and losing its sheen. Check for fastness, especially with the darker colors.
Metallics - Period metallic threads in embroidery were generally either thin gold foil on a fiber core or various metal wire preparations. Japan thread makes an excellent approximation of wrapped silk for couching. Real gold, gilt, and plated buillions of various shapes are also available.
Rayon - This synthetic floss has a sheen more dramatic than even silk. It's very strong, and makes a statement. Rayon isn't period, but can be useful, especially for favors that are likely to suffer abuse. It can be a frustrating fiber to work with due to its tendency to knot, snarl, and curl. This can be tamed by wiping the working thread down periodically with a damp cloth.