No, there is such a thing as absolute morality. It's just that nobody can get it right because pure morality is highly complex in relevance to the general idea of right and wrong.
We are too imperfect as people to have the logic, as we practice immorality everyday. Simply by flushing the toilet or taking a 20 minute shower, you are contributing to the immorality of millions of people around the world without water.
Self-importance makes the world go around, not morals.
This, while I do believe with Darquewillow's sentiments about not needing a God to be moral, I have to say morality at best is a highly complex term. We have set a societal limit on what exactly is immoral and what is universally accepted as moral through what we call "laws." Stripping it directly from the religious texts we have: 'don't kill,' 'don't steal,' 'don't covet another man's objects/wife/girlfriend/ friend/ etc.,' 'do not cheat,' etc.
Essentially organized religion, particularly Christianity, I've found (sorry if I offend any highly religious Christians) has its own reward system. You have a reward and a punishment for every transgression you commit and for every good deed you commit. So if you were to give a homeless man the clothes off of your back that would make you morally correct, for you have a done good deed. Tally that up over your lifetime and you will, according to the Bible, find yourself at Heaven's Gate. It's a highly, in my opinion, flawed system because the morals of a person can vary greatly depending on the way their life choices shaped them.
So this brings me back up to my earlier example: What if you were that homeless man and you had no money, no food, and no clothing? What if you had to scavenge around in garbage cans, eating the scraps of food that thousands and millions of people discarded so carelessly? What if you were dying from some sickness, had no health insurance, no job, and you had to resort to stealing medication just to live? By society's limited standards on morality, stealing would be seen as immoral. But as a poor man just trying to get by, you would see this as morally acceptable because it's a matter of survival. Certainly you wouldn't want to steal, at some point you may have had a job and money and somewhere along the course of your life you may have lost it. The difficulties of society may have pushed you into committing something you may not have wanted to do: steal medicine for yourself or a dying relative because you severely lacked the funds to get it.
In situations such as this and many others, the definitive meaning of morality is questioned.
But humans, particularly religious ones must feel the need to complete a moral deed for some sort of reward. Getting into heaven or depending on a higher and ultimately more intelligent deity makes us more comfortable doing something that is considered selfless. Doing something immoral such as lying, stealing, cheating, killing, etc. will supposedly get you into Hell.
And yet, we as human beings have a wonderful ability to embrace Free will. We can do as we please, if we struggle to survive then we can live off of instinct: smuggling food, searching ceaselessly for a job to earn monetary funds to thrive. We can put our mothers and fathers in nursing homes, having the state's taxes fund for their care, or we can take up the burden upon ourselves. We can choose to steal food that we never bought with our own money that was thrown away to get a meal or we can struggle to find a job to make ends meet.
What we find to be moral is a perplexing thing because this depends upon the individual. As a child, your parents may or may not have taken you to Church and what you learned to be morally acceptable and immoral would have come to you from the mouth of a preacher and from a Holy Bible or the Quran or the Torah or some other form of a religious text. And yet as, Jquestionmark said, as you mature and view the hardships of other people: relatives, friends, strangers on the street, as well as the difficulties you face in your own life, your view of morality will be reshaped.
I personally believe that morality should not be determined by what you read in religious book but should be defined by what you as an individual perceive it to be. I give the clothes off of my back to children suffering from Lupus because I choose to, not for some petty reward or recognition. I neither expect a pat on the back of a "good job" from someone who knows this obscure fact about me, because regardless of what they think it's something I want to do, that I feel obligated to do. If I donate blood to someone it's because I want to, because the moral for me is a positive one.
I'm partly a follower of what society dictates as immoral and moral and yet I feel that if you are poor and you have no other choices granted to you, then sleep on a public bench, scavenge for food, beg for money, do what you must to survive. Your morals are your morals and so not only is it complex, broad, and transient in its definition, but it also can not and should not be adamantly restricted to what society and its laws govern.