Are there any non-green, non-artifact mana ramp cards?
There are, but they are purposefully few and far between.

Mana acceleration is considered to be in green's part of the "color pie," with the exception of the occasional black card, and a little bit of a fast-mana theme in red (formerly black). Blue and white occasionally get ways to cheat on mana a bit, but only when they're tied into some other element of those colors.

This answer has discussion tailored to Commander, which also applies pretty well to other casual and multiplayer decks.

In competitive terms, the most relevant cards are:


Dark Ritual is the classic mana acceleration card, in black. It's still an influential card in Legacy.
High Tide features in Legacy blue decks. The trick with this is to take one "big turn" where you develop tons of mana by playing cards that untap your lands, like Time Spiral and Candelabra of Tawnos.
In Modern, Desperate Ritual, Pyretic Ritual, Seething Song (this one's banned at the moment) &mdash; along with Manamorphose, which actually gives you extra mana if you have a cost-reducer or copy-card in play &mdash; are commonly played in storm decks.
In formats with fetchlands, Deathrite Shaman is a mana dork that doesn't actually require a green deck to work very effectively.


Note that there are a lot of colorless cards that are used to cast normal colored cards (like Ancient Tomb).   

Also note that oftentimes it's more effective to "cheat" on costs (using reanimation or hand-to-play cards like Show and Tell) than to accelerate your mana.