According to I Timothy 2:4 (NIV), God "...wants all people to be saved and to come to a knowledge of the truth".
But since we have free will, God cannot make us choose to accept the salvation that is available through his Son.
Since I believe that God loves others more than I can, and he desires them to be saved. I think it's logical to conclude that he's going to do everything He can to draw them to Him.
So then what is the point of praying for someone's salvation?
Even if we can't pray away someone else's free will or convince God to bend the rules regarding the requirements of salvation, there can still be merit in praying on behalf of others with a slightly different attitude. Perhaps "let them have experiences that will lead them to the truth," or "let their hearts be softened, that they may give heed to the Holy Spirit and accept the truth when it is presented to them" would be more appropriate.
And, as JustinY pointed out in his comment, praying for the welfare of others can be beneficial to us. Simply because we pray to God for something to happen doesn't mean we can't directly take part in bringing such a prayer to fruition. If we seek to truly pray in Jesus's name and harmonize our will with his, it will lead us to be more conscious of the spiritual needs of others in our day-to-day lives, and to find effective ways to bring others to Christ.
In John Piper's talks on Calvinism, he addresses this very point - why pray or even evangelise the non-saved since God has already elected who will be saved and who not.
His answer is that our action is the means by which God often achieves His will. So if God has ordained that Bob will be saved through the witness of Jim, then Jim will witness and Bob will be saved. However, if Jim decides out of fear not to share the Gospel with Bob, this doesn't necessary mean that Bob will not be saved - just that Jim has decided to neglect His Christian responsibility to witness and God may or may not have someone else planned to witness and still bring Bob to salvation.
Please note that this answer is not saying:
It is a tremendous opportunity to be a part of God's saving work, and our actions do have very real consequences. Unconditional Election teaches that God chooses the person unconditionally (that is, the person himself/herself has not merit), but this doesn't mean that God doesn't use our actions/choices in determining who will be reached and ultimately, saved.
Lastly, it is obedience on our part - we're told to preach the Gospel and pray for unbelievers, regardless of whether we understand the behind-the-scenes work that God does in reaction to our prayers.
In Luke's gospel, Jesus informs Simon (Peter) that Satan had desired to try his faith to the verge of overthrow, but that, through the prayers of Jesus, his faith would be strengthened. He was further admonished to do the same for his brethren (strengthen them) once he had been converted (see Acts Chapter 2).
Luke 22:31-32 And the Lord said, Simon, Simon, behold, Satan hath desired to have you, that he may sift you as wheat: But I have prayed for thee, that thy faith fail not: and when thou art converted, strengthen thy brethren.
It is true that God, being "a gentleman", will not force someone to do something they don't want to do (i.e. override their free will). But prayer will thwart the plans of Satan and pave the way for a wayward one's heart to be turned home.
The confusion comes in when we conflate "salvation" with "ending up in Heaven for eternity."
"Salvation" has three meanings in Scripture:
Initial conversion (being "born again")
Sanctification (of believers)
Ultimate redemption (resurrection, etc.)
It is clear that the first two can happen without the person necessarily ending up in Heaven for eternity, given the many passages that clearly show that a person can "fall away". (Really, a case could even be made to include the last sense of the word as well based on passages like Matthew 22:1-14.)
Who ends up in Heaven for eternity? Only God knows, but we can trust that He is just, so we don't really need to worry about messing that up. Truth be told, I'm not even convinced a person has to be born for Him to make this decision justly. (See here for more.)
With that said, the value in praying for someone to "get saved" or "continue to experience salvation" or "be saved on the last day" is the same as the value in praying that an unbeliever would experience a clear sign from God, or begin to seek God, or recognize that God is trustworthy.
It is good to experience the kindness of the Lord. If you love them (which you should), you should do good to them and desire good for them.
You can join God in His efforts to draw His "lost sheep" to Himself. God's preferred method of blessing is often via the prayers of His people.
Even if you pray and they "get saved", but the person never ends up in Heaven for eternity, at the very least they will have no excuse on judgment day.
So, in summary, the value in praying for a person's salvation is the same as the value in praying for any good thing for another person; It is loving, it is partnership with God, and it is a witness to the "wicked".
