Are there any tenets of Gnosticism that are still present in the church today?

Gnosticism was a movement that sprung up as an attempt to fill a major knowledge vacuum in the Scriptural record. The Gospels record that even the Apostles, Jesus's highest and most trusted disciples, were spiritually weak and deemed by the Lord as unready for the true doctrines of the Kingdom.

For example, witness Peter, who boasted of his fearlessness and readiness to follow the Lord to any tribulation, only hours before being reduced to fearful lying to disassociate himself from Christ when the actual tribulation came. The "fearless" apostle, the one who Jesus had named the Rock, was reduced to cowering before a serving girl, one of the lowest social positions in Jewish society!

But all that changed once they began their ministry. Acts describes Peter as a preacher of true fearlessness, ready to face prison and beatings and all manner of tribulations for the Lord's sake. And as for what happened to change him and the Apostles, we are left with a void. The Scriptural record glosses over the events that occurred after the resurrection.

We are told that the resurrected Christ talked with two disciples on the way to Emmaus,

And beginning at Moses and all the prophets, he expounded unto them in all the scriptures the things concerning himself.

but only the first few sentences of this wondrous sermon are preserved for our knowledge. Likewise, Luke records that "also he shewed himself alive after his passion by many infallible proofs, being seen of them forty days, and speaking of the things pertaining to the kingdom of God." (Acts 1:3) but the record is silent on the contents of this teaching. Any understanding of Gnosticism has to take this into account, for it is the root of Gnosticism. Dr. Hugh Nibley wrote:

All the 40-day teaching is described as very secret, delivered to a closed cult group. There is no desire to intrigue and mystify, however, as with the Gnostics, but rather the clearly stated policy that knowledge should be given always but only to those who ask for it, with the corollary that the higher and holier a teaching the more carefully it should be guarded. As "the last and highest revelation," the teaching of the 40 days was top secret, and has not come down to us. Since Irenaeus, churchmen have strenuously denied that there ever was a secret teaching or that anything really important has ever been lost. To profess otherwise would be perilously close to an admission of bankruptcy; yet Christian scholars do concede that the Apostles had information that we do not have, allow the existence of an unwritten Apostolic tradition in the church, and grant that there was a policy of secrecy in the early church—though insisting that it began with the catechetical schools. The catechists, however, appeal to a much earlier tradition of secrecy, and when the Fathers attempt to reproduce the unwritten tradition which they claim for the church they have nothing to offer but the commonplaces of the schools. Plainly things have been lost.

After the alarming gap in the record following the fall of Jerusalem, the curtain rises on a second-century church seething with conflict and split into factions hotly debating the reality of the Resurrection. The Gnostic exploited both the ignorance and the knowledge of the time—the knowledge that the answers to the great questions of existence were known and treasured by "the Elders" of another day, and the ignorance of just what that knowledge was. The oldest definition of the Gnosis specifies that it was the knowledge imparted secretly by the Lord to the Apostles after the Resurrection. The Gnostics claimed to have that very knowledge, and their tremendous initial success shows how hungry the Christian world was for it—the "main church," in fact, had to invent a counter-Gnosis of its own to meet the threat and ended up with a compromise that has left a Gnostic stamp on Christian thinking ever since. The Gnostics did not invent the 40-day situation, as has been claimed, for they were the last people in the world to imagine a return of the Savior in the flesh, and any tinkering would have been readily exposed in a quarreling and hyper-critical society; but they did exploit it because it was there and they had to: at a time when everything else was being questioned, it is one of the few things that is never challenged.

With this knowledge unavailable to the church in general, but its existence unquestioned, false teachers sprung up to fill the void, bringing a new doctrine inspired heavily by Greek philosophy. The idea was that physical matter was somehow corrupt and evil, and that God's plan involved freeing Mankind from the bonds of the flesh.

If you're looking for Gnostic influence in modern Christianity, you need look no further than this basic concept. A lot of the more "out there" Gnostic teachings have been stamped out, but shades of the core ideas can be found even today in the common understanding of God as a being of pure spirit, without any physical form. The Christ of the Bible, and of the early Christian church, was a resurrected being who went out of his way to prove and demonstrate that he had a fully real body of flesh and bones!