Dreams mean things to us because they can help us "see into the future" (precognitive dreams). If they don't mean anything, how can we "see into the future"? Dreams can also just be a mash of random thoughts and feelings that don't really mean much. However, it is still personal to us.
On the personal level for sure dreams mean a lot and help the person work out issues in his or her life. But if Carl Jung was right and a larger mind is being channeled through our brains, they also mean a lot in terms of reflecting deeper meaning and revealing the collective unconscious.
Yes, dreams mean things, because they show what we are thinking in our subconscious. Dreams show what we are thinking but we are afraid to say. They show our innermost fears. Dream mean a lot because they show what we do not think that we can say. Dreams help us conquer ourselves.
Yes, I believe that dreams mean something some of the time. Granted, they are almost always your brains way of dealing with the stress you encountered throughout your day, but sometimes, you just know your dream is different. How many times has someone not gotten on a plane or train because their dream warned them not to, and then the plane or train crashed? How many times have you awakened from a dream and known not to do something you had planned?
I have had many dreams in my life time and I have taken medication that makes those dreams more violent. The fact that my dreams can be influenced by medication leads me to believe that the dreams are meaningless. I like to dwell on my dreams sometimes and some have stayed with me for decades, but that doesn't mean they have a purpose.