Single Party Encryption, Multi Party Decryption
Check out Pedersen's scheme for threshold ElGamal (link). Also, check out (this) for an application to electronic voting.

Basically, the scheme works like this. There are $n$ parties, out of which at least $t$ must be reliable or else the scheme collapses. They choose a prime $p = 2q + 1$ where $q$ is also prime, i.e.: $p$ is a safe prime. Additionally, they choose a generator $g$ of the $p$-order subgroup.

Every participant $i$ chooses a polynomial $f_i(x) \in \mathbb{Z}_q[x]$ of degree $t-1$ and privately distributes the points $f_i(j)$ to each participant $j$. Each participant $j$ adds together all the points he received: $f(j) = \sum_if_i(j) \mod q$. The participants have now shared a global polynomial $f(x) = \sum_if_i(x) \mod q$ which is uniquely defined by $t$ points. The secret is located in $f(0)$.

In order to make the scheme verifiable, each of these private shares $f_i(j)$ is accompanied by a public commit value $g^{f_i(j)}$. Each participant is commited to his share $f(j)$ in the global polynomial as $g^{f(j)} = \prod_ig^{f_i(j)} \mod p$ is publicly known.

In order to raise a value $h$ to the power $f(0)$, the participants do the following. Each participant raises $h$ to the power of his own share. They publish $h^{f(i)}$ along with a Chaum-Pedersen proof (link) that the exponent in this value with respect to base $h$ is the same as the exponent in the commit value $g^{f(i)}$ with respect to base $g$.

Anyone can now combine the shares and calculate using Lagrange interpolation $g^{f(0)} = g^{\sum_if(i)\prod_{j \ne i}{-j \over i-j}} = \prod_i(g^{f(i)})^{\prod_{j\ne{}i}{-j \over i-j}} \mod p$.

The indexes $i$ and $j$ run over any set of at least $t$ trustworthy participants. This exponentiation procedure is used once for key generation and once for ciphertext decryption. Note that this allows an arbitrary order of contributions from the participants, so long as at least $t$ participants remain uncorrupted. For the rest we follow the regular ElGamal cryptosystem.