I would say that's normally the case. I think your subconscious mind is at work or at play during your dreams. I sometimes dream about work, and my mind is playing out potential scenarios for situations that are likely to occur.
I can remember more than once when I was at work on a piece of writing, and hit a snag, only to wake up from a dream with the answer. I had to write it out because it was perfect. The one I remember most vividly was a piece of iambic pentameter poetry that was frustrating me because the right words were just elusive enough to evade my ponderings. I woke up in the middle of the night, and the whole poem was complete, just as I had dreamed it. I never changed another word.
I do think that dreams can serve as warnings... I have heard many stories of dreams that served as forewarnings of danger, and I have known some of the people that had those dreams... in a couple of cases, I was told the dreams before the events in the dream happened, so I believe that there is something beyond one's own mind that can influence the shape of dreams, but I don't think this is normal. Generally, I believe dreams are the product of the subconscious mind.