Well decohernce can be put into just about any quantum interpretaion, it's more a process than an actual interpretation.
True, but there are some people (notably Zurek) who think environmental decoherence ALONE can provide an explanation of quantum mechanics. In this sense it can be regarded as a separate interpretation.
No-one has mentioned "spontaneous-collapse" models yet, although you might want to put them in the "realist" category. However, there is a distinction to be made between whether you are being realist about particle properties (e.g. positions as in Bohmian mechanics) or wave-properties (as in spontaneous collapse models). You could also be realist about something much more abstract, such as quantum logic, but these interpretations usually end up having a somewhat positivist flavour that makes the 'realist' label a bit of a misnomer.
There is also something called the "new orthodoxy", which is a modern non-interpretation designed to replace the Copenhagen non-interpretation. Copenhagen is actually untenable nowadays because it postulates a divide between the classical and quantum worlds, without saying where this divide is to be found. However, as experimentalists can now do quantum mechanics with macroscopic systems it doesn't really make sense to have this divide at all. Therefore, the "new orthodoxy" runs something like:
A) Quantum mechanics applies to all systems in the whole universe.
B) We don't see Schrodinger's cat in a superposition because of environmental decoherence.
C) The wavefunction appears to collapse in a measurement due to the same sort of effect.
Of these three, (C) is the most problematic, but it allows most researchers to get on with their work without worrying about foundational issues, much as Copenhagen did for most of the 20th century.