Context-Free Languages where every rule produces at most one non-terminal
A grammar where every production has at most a single non-terminal is called a linear grammar. If the non-terminal is rightmost in all productions, it is a right linear grammar; if the non-terminal is leftmost in all productions, it is a left linear grammar. Left and right linear grammars produce regular languages (and every regular language can be described by a right and a left linear grammar), but unrestricted linear grammars produce a proper superset of regular languages ($a^nb^n$ is linear), are not necessarily deterministic (the set of palindromes is linear), and are a proper subset of context free languages (the Dyck language [Note 1] has no linear grammar. The Dyck language has a deterministic grammar, so linear languages​ are not a superset of deterministic languages, either.)
It is not decidable whether a CFG has a linear grammar, a result proven by Sheila Greibach in 1966 (http://dl.acm.org/citation.cfm?doid=321356.321365)

Notes

The Dyck language is the set of all strings of square brackets where the brackets are balanced, given by the deterministic CFG:

$$S \to \epsilon \mid \mathbb{[}\; S\; \mathbb{]} \; S$$