In past times and in diverse manners God spoke through prophets. Of course, this is how we believe the Bible was produced and compiled so, as a few answers and comments have pointed out, the Bible itself is excellent proof of personal revelation by the Holy Spirit.
God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets, Hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds; Who being the brightness of his glory, and the express image of his person, and upholding all things by the word of his power, when he had by himself purged our sins, sat down on the right hand of the Majesty on high; - Hebrews 1:1-3
However, it is to be noted that this is contrasted with "in these last days'. The same God who spoke, in past times, through prophets has now spoken through His Son. As the Son has fulfilled the office of Priest such that the priesthood and the altar service of the temple is obsolete, in like manner the Son fulfilling the Prophetic office has made prophets obsolete. John the Baptist, last of the Old Testament style prophets has made this clear:
Ye yourselves bear me witness, that I said, I am not the Christ, but that I am sent before him. He that hath the bride is the bridegroom: but the friend of the bridegroom, which standeth and heareth him, rejoiceth greatly because of the bridegroom's voice: this my joy therefore is fulfilled. He must increase, but I must decrease. - John 3:28-30
So we are not to expect any more prophets of the Old Testament style; prophets who bring forth new doctrine-producing revelation from God. Everything spoken that way has been fulfilled, expounded upon, and reinforced by and through the Son. What the Son has done is to open the OT Scriptures, which speak of Him, to our understanding through the Holy Spirit:
And the Father himself, which hath sent me, hath borne witness of me. Ye have neither heard his voice at any time, nor seen his shape. And ye have not his word abiding in you: for whom he hath sent, him ye believe not. Search the scriptures; for in them ye think ye have eternal life: and they are they which testify of me. And ye will not come to me, that ye might have life. - John 5:37-40
This is, if you will, the New Testament prophetic office: The continuing opening up to our understanding of the immeasurable depth of what God has spoken first through His prophets and finally through His Son. Passages which speak of prophecy in the latter days is of this sort: In these last days He has spoken through His Son and the Holy Spirit is sent to remind us of everything He has said:
“These things I have spoken to you while I am still with you. But the Helper, the Holy Spirit, whom the Father will send in my name, he will teach you all things and bring to your remembrance all that I have said to you. - John 14:25-26
The limitations (and the warnings) that are placed upon us are the same limitations that our Lord applied to Himself in taking on humanity; do not go beyond what is written. He did not develop new doctrine when tested by Satan in the wilderness but withstood him by what was already written:
But he answered, “It is written, “‘Man shall not live by bread alone, but by every word that comes from the mouth of God.’” - Matthew 4:4, etc.
And when He taught in a "you have heard it was said ... but I say" fashion (sermon on the mount style) He was not adding to or producing new doctrine but deepening, intensifying, and personalizing what was already written.
Therefore, at least from an evangelical standpoint, any personal private revelation which contradicts something that has already been written or does not deepen understanding of who Jesus is and what Jesus does (according to what is already written) is to be held as highly suspect at best.
We are wayward in disposition, hard of heart, and prone to desire teachings that tickle our ears. If the Lord Jesus Christ saw the Old Testament as sufficient for His purposes as a human and if the Apostles encouraged folks to examine those same Scriptures to validate what they were saying then we should be humbly content with what we have and stand fast against new and contradictory information from 'modern day prophets':
Now these Jews were more noble than those in Thessalonica; they received the word with all eagerness, examining the Scriptures daily to see if these things were so. - Acts 17:11
There is no room, biblically speaking, for the appearance of a new prophet with new or 'restored' doctrines of either faith or salvation. Whatever appears apart from congruence with what we already have is not from God:
Beloved, although I was very eager to write to you about our common salvation, I found it necessary to write appealing to you to contend for the faith that was once for all delivered to the saints. - Jude 3-5
