What asymmetric key exchange algorithms are known besides DH? On Wikipedia, a lot of the subjects that are said to be different key exchange methods are often just protocols that incorporate the Diffie-Hellman algorithm into them. The only other key exchange algorithm I know of besides DH is Algebraic Eraser, of which I don't know much about. Are there any others? And I don't mean key exchange schemes based on symmetric key primitives.
Using lattices/ring-LWE, there is Lattice Cryptography for the Internet (by me), which inherits from Ring-LWE encryption, and has been implemented by Bos et al. with further improvements by Alkim et al.

The underlying mechanism is conceptually DH-like, but uses completely different mathematics.  We start with a uniformly random $a \in R_q = R/qR$, which can be chosen by one of the parties or by a trusted third party.  Here $R$ is an appropriate choice of ring, e.g., $R=\mathbb{Z}[X]/(X^n+1)$ for power-of-two $n$ (in the few hundreds, for current security estimates).

The basic protocol works as follows (oversimplifying a bit): to establish a key, the first party chooses a "short" random $e \in R$, and announces $E \approx e \cdot a \in R_q$, where the approximation hides some short random error.  Similarly, the second party chooses a short $f \in R$, and announces $F \approx a \cdot f \in R_q$.  The first party can then compute $e \cdot F \approx e \cdot a \cdot f \in R_q$, and the second party can compute $E \cdot f \approx e \cdot a \cdot f \in R_q$.  The parties then use some kind of "reconciliation" mechanism to extract a common secret key from their shared "noisy" versions of $e \cdot a \cdot f$.

The above mechanism can be proved secure against passive eavesdroppers assuming the hardness of the corresponding Ring-LWE problem (which itself can be proved quantumly as hard as worst-case problems on ideal lattices, for appropriate parameters).  Of course, in reality we need authenticated key exchange and other properties; these can be obtained using additional techniques that originated in the DH setting (see the first link for details).