Still water (in a container)
Relatively still water contained in a container - for example a swimming pool - is simulated in many games, for example Half Life 2. It simulates light objects like wood floating up to the surface, while heavy objects may sink slowly to the bottom etc. There may also be waves on the surface.
This type of water physics can be simulated in Unity without problems (2.x or 3.x, it doesn't matter), it just requires some scripting with AddForce() and such. Basically, whenever an object is below the water surface, add an upwards force corresponding to the buoyancy of the object. When the player or other objects collide with a floating object, be sure to make the impact use AddForceAtPosition() rather than AddForce() in order to get a realistic floating feel, where object may tip over.
As for adding waves, waves can either use a predefined pattern based on a texture, or sinus functions, or waves can be simulated to reach realistically to disturbances in the water. See this post for the latter.