A very generic question
It is very hard to answer this question because it is very generic.
In order to get a clearer answer you'd have to narrow down your definition of what exactly constitutes subliminal message and what exactly constitutes an effect.
Once done, you can now talk about specific types of stimuli processed purely by the subconscious, and their specific effect and related variables.
Here are some examples of what might constitute 'subliminal messages':
- A metaphor
- Asking someone to hold a warm cup of coffee
- Putting an image of eyes in the room
- 'planting' a video frame in a sequences of other frames
The effect (and the extent) of all of these depends on the 'message' itself and the specifics of the experiment.
You can read further about this 'complexity' simply by reading Wikipedia's entry on Subliminal Stimuli (and the references therein).
A very generic answer
Without specifics, you can argue the following:
There is mounting evidence that pure subconscious processing can affect our behaviour, albeit often short lived.
I could point you to many resources dealing with specific cases, but I think you'll find much of what you're after (or at least a good subset/overview) in the first couple of chapters of this book:
Dehaene, S., 2014. Consciousness and the brain: Deciphering how the brain codes our thoughts. Penguin.