As others have pointed out, there are many places in the Bible where believers are encouraged or even commanded to pray. So from a Biblical point of view, the question is not, "Should we pray?" It is fair to ask, "Why should we pray?" or "What is the effect of our prayers?"
Luke 18:1-7 (NKJV): Then He spoke a parable to them, that men always ought to pray and not lose heart, saying: “There was in a certain city a judge who did not fear God nor regard man. Now there was a widow in that city; and she came to him, saying, ‘Get justice for me from my adversary.’ And he would not for a while; but afterward he said within himself, ‘Though I do not fear God nor regard man, yet because this widow troubles me I will avenge her, lest by her continual coming she weary me.’” Then the Lord said, “Hear what the unjust judge said. And shall God not avenge His own elect who cry out day and night to Him, though He bears long with them?
God wants to do good things for his children. You could say that he already knows what we want and need and so there is no point in telling him. But then we get into logical conundrums. You could say that God is all-knowing and so he knows what you would have asked for if you had asked. But then you're saying, not that God knows everything that happened, but that he knows something that might have happened except for the fact that it didn't happen. If we never vocalize what we want, have we even thought through in our own minds what we want?
I -- like, I am sure, many other Christians -- am confused by John 14:13, "And whatever you ask in My name, that I will do." It certainly SOUNDS like it means that God will give us anything we ask for. But we all know from personal experience that that isn't true. Far more people have prayed to win the lottery than have won the lottery, etc. Lest someone say that that's because we're deluding ourselves in thinking that we are among the saved, surely we would all agree that Paul was saved, and yet Paul said, 2 Corinthians 12:8-9 " Concerning this thing I pleaded with the Lord three times that it might depart from me. And He said to me, “My grace is sufficient for you ..." In context, Paul had some sort of medical problem -- scholars debate just what it was, but it doesn't matter for this point -- he prayed three times that God would heal him, and ... God didn't heal him. So God did NOT give even the faithful Apostle Paul everything he asked for.
(And lest an atheist say, "Aha! Another false statement in the Bible!", surely everyone who read the Gospels when they were first written knew that Christians don't get everything they pray for. If the Bible was really written by people trying to pull off a huge hoax, why would they deliberately include a statement that said something that everyone who read it would instantly know was not true? If I was writing a book trying to convince people that I had been kidnapped by aliens, surely I would say that this happened in an isolated place far from civilization in the middle of the night, so no one could prove me wrong. I wouldn't say it happened on the 50-yard line during halftime at the Superbowl.)
So bringing those two points together: If God is all-knowing and all-wise, than he presumably could form a perfect plan. But if one of his goals is to make his children happy, then it follows that his plan must take into account the wishes of his children. Of course God is all-knowing and we are not, so sometimes our wishes are, in fact, bad for us. A wise and loving God won't give us things that he knows will hurt us. But given many possible good things, he can give us the thing that we want. It's like parents giving birthday presents to their children. If a 6 year old says, "I want a machine gun for my birthday", a wise parent is not going to give it to him just because he asked for it. But if the parent is deciding whether to give the child a baseball or a toy train, what the child wants would likely be a major deciding factor.
To take the silly extreme, if you pray, "God please help me to kill my neighbor because he annoys me with his loud music", I doubt that God will grant that prayer. But if you pray, "Help me to get a job as an accountant" versus "... as an auto mechanic", he might well honor that, as the difference may well be purely a matter of what you enjoy. Then again there may be larger implications that you don't know about. I've had a few times in my life that I've prayed for something, it didn't happen, and I've been frustrated and disappointed, and then sometime later I saw that if I had gotten what I'd asked for, it would have been bad for me. I'm sure there have been other times when I've never realized why it would have been bad.