I have experienced a few different kinds. My grapheme-> color perceptions (meaning that I perceive letters and numbers in color) are always around. I have a theory that it's the reason I'm such a good speller-- I remember words (and phone numbers) by the sequence of colors in which they appear behind my eyelids. Weirdly, numbers have a stronger color association than do letters for me, even though I'm a word person and not a math person at all. That's what my numbers look like, on the left.
A lot of my numbers and letters are different shades of that yellowy-orange. I don't know why, because the color actually sort of pisses me off. I also experience the year as a mobius strip around my body, with January behind me and to the left. I've realized that when I talk about a particular time of the year, I gesticulate in the direction that I perceive it to be. I wonder if anybody notices.
When I smoke kief, things start to get weirder, and I occasionally get other forms. Once, the textures that I touched produced color in my head. I thought that it was so cool that I made a painting (with Q-Tips and nail polish) of the colors that I touched.
In addition, because of my psychedelic experiences, I occasionally taste music. I think that this is a permanent change, but it has to be the right kind of music. During my first acid trip, I was enjoying the song Spitting Venom by Modest Mouse and suddenly I could feel it like pop rocks on my tongue.
It was the coolest sensation, but I figured it was an isolated incident and forgot it for about two months. In between, I did no additional psychedelics, aside from marijuana once a week or so. I was sitting on my bed listening to Radiohead's Hail to the Thief, and the flute that was woven through the song kept causing an actual physical sensation of pain in the center of my tongue, like being poked with a needle. I got so annoyed with that sensation that I had to turn the music off, even though I really enjoyed the sound of it. Since then, I occasionally have a sense of pressure on my tongue, and a related taste of copper pennies, when listening to music.
I love my synesthesia, despite the occasional unpleasantness. I feel lucky to have such a unique way of experiencing the world. Unfortunately, even though drugs have given me new sense combinations, my natural synesthetic perceptions are getting weaker as time goes on, and I don't know how to preserve it. It probably has something to do with all the playing that I do with my neurochemistry, but I like those games too much to stop. :)