As @DavidH points, if there are no consequences there are no actions. There are no reasons to perform those actions either, and there are no reasons to behave in one way or another if people are not encouraged to do so.
While the answer is technically correct, I don't consider it a good answer because I think it fits a question that is misleading due to its wording. Therefore I'm going to propose a different wording, that leads to a more interesting question and more interesting answers: Should people be moral if there is no explicit incentive for morality?
Now that's a different thing. Should people try to do well to others or the planet (ecology) even if there is no God, government or any Big Brother there to reward them for their good actions?
The answer is yes, for many reasons, but all of them boil down to game theory, at least all the reasons I can speak of.
Basically altruism is an indirect reward that is expected to pay back when properly done, and from which we are benefiting since the moment we are born. So there is a culture of altruism, a tacit agreement that we are interested in preserving, because we get more from it than what we have to pay.
The morals that are to some extent encoded in most of us (possibly in our DNA, except psychopaths) are a way to get through local maximums. An example of a local maximum can be found in the tragedy of the commons, in the prisoner's dilemma, and in most games that are interesting from a game theory perspective.
These tacit agreements provide more utility in their results than the lack thereof, or they should do so to endure. They can also be traditions that should be forgotten because they were once useful and now harmful. E.g. We have now cheap and good contraceptive methods, so maybe some traditions about sex could be broken.
That's why it is important to know the roots for the morals, if they are currently beneficial, and judge critically.
To summarize, to the question, "why should I respect other people if I don't get a cookie for it?" The answer is: because you will promote a culture of respect in which you will live. Also, you never know when you are going to find a psychopath that may be violent, it's usually wise to avoid useless trouble.
I'm also going to add two examples.
You may not take care of the light bulbs in your house, but after some time your future-self will be in the dark for your irresponsibility. This example can be expanded gradually from your house to your planet and beyond.
You may be a tourist in a foreign country and not care about what they think about you, but their prejudices are going to be unavoidable (we are humans) and they are going to use the information about the people from your country that they have seen before. If you all behave well you all will be rewarded indirectly (some people for some other people) and viceversa with the punishments. It's like having a few stocks (that you can't sell) on a big company, the intelligent option is not to harm the company uselessly because its benefit is your benefit to some extent. This can be considered analogously in many other circumstances, not only tourism.