Let $\mathcal{X}$ be an algebraic space. Can it happen that there does not exist a map $\mathcal{X} \to X$ with $X$ a scheme that is initial for maps from $\mathcal{X}$ to schemes? Are there reasonable conditions (e.g. finite type) that we can put on $\mathcal{X}$ so that there does exist such a universal map to a scheme?