Real world use cases of Multi-Party Computation
As I mentioned in a comment, a relatively new application of multi-party computation is its use as a countermeasure against (mainly hardware) side-channel attacks. In particular, there is a method called "threshold implementations" which is based on a form of secret sharing.

A relevant reference would be the paper Secure Hardware Implementations of Nonlinear Functions in the Presence of Glitches by S. Nikova, V. Rijmen and M. Schläffer.
Extensions to higher-order DPA attacks have also been proposed.

Let's say you wish to securely implement a Boolean function $f$ with $n$ input bits. The (secret) input $x = (x_1, \ldots, x_n)$ is then "shared" by (randomly) choosing additive shares $x_{i, j}$ such that

$$x_i = \bigoplus_{j = 1}^{s_{in}}x_{i, j}.$$

I'll write $\mathbf{x} = (x_{1, 1}, x_{1, 2}, \ldots, x_{1, s_{in}}, x_{2, 1}, \ldots, x_{n, s_{in}})$ for convenience below.

The idea is then to share $f$ too, in such a way that for all inputs $x$ and correct sharings $\mathbf{x}$

$$f(x) = \bigoplus_{i = 1}^{s_{out}} f_i (\mathbf{x}).$$

This is called the correctness property.
We now also require that $f_i$ is independent of every $i$th share of $x$. So each $f_i$ actually operates on $n(s_{in} - 1)$ rather than $ns_{in}$ inputs. This is called the non-completeness property.

Under the non-completeness assumption, the paper shows that if $x$ is shared with independent uniformly chosen shares, then $f_i$ (as well as any intermediate result) is independent of the input shares $x_{k, i}$ with $k = 1, \ldots, n$.
This then leads to pipelined implementations which are secure against first-order (i.e. using first-order statistical moments) side-channel attacks. For more details, take a look at the paper (or other papers on the same subject).