How did the Inquisition impact modern Christianity? Related Question
  
  How did the Crusades impact modern Christianity?



How did the Inquisition impact modern day Christianity own sense of morality and spirituality?
What do these things mean to a person of faith?



  The Inquisition, Inquisitio Haereticae Pravitatis (inquiry on heretical perversity), was the "fight against heretics" by several institutions within the justice-system of the Roman Catholic Church. It started in the 12th century, with the introduction of torture in the persecution of heresy. Inquisition practices were used also on offences against canon law other than heresy. (Wikipedia)
I'm addressing all of the inquisitions, not merely the Spanish Inquisition here.  Several were perpetrated by kings, not the Catholic Church.

I agree with the other answers that state that the Inquisition is a stain and an evil that should never have happened.  None of what I'm posting here should be taken in any way that detracts from @James Black's answer, or @Apocatastasis.  I'm merely listing some impacts not listed in their answers.

Impacts include:


A tendency to view Church authority with skepticism, particularly when we smell an abuse of power

For me, personally, this is why I tend to lean on the words of Scripture, which never changes, as opposed to religious teachings of any one denomination.

A cadre of anti-theists, who object to Christianity, among other reasons, on the basis of the fact that the Inquisition happened. Examples:  1  2
A rise in atheism, anti-theism, antireligion, and other beliefs based on the assumption that since the Inquisition(s) were perpetrated by "Christians" that Christianity supports such atrocities. (see previous references)

It doesn't.  At least not if you believe that Jesus taught that we are to love our enemies as well as our neighbors
I also personally think that  just because these officials were self-described Christians, their actions show that they had no idea what it means to be a Christian.

Christians that are stronger in their views of the importance of God's commandment to love our neighbors (and our enemies) because we have such a stellar (if horrific) example of how not to treat those who disagree with us. examples: 1 2
Christians and non-Christians alike that are better educated and on guard against such abuses, because as long as human nature is what it it, it could happen again if we're not vigilant. example: 1 

Unfortunately, this isn't the majority.  Just like all other generations, we think we're so much more enlightened than they were in the past.  We're not.  The Germans refused to believe what the Nazis were doing because they thought it couldn't happen in their society.  If we can't learn the lesson that people are corrupt and it can happen as soon as we let our guard down, it will happen.  Time and time again. 



Also, if my understanding of the history and timelines is correct, then at least some of the Inquisitions happened before or during the Protestant Reformation.  


Medieval Inquisition - 1184
Spanish Inquisition - 1480
Protestant Reformation - 1517


Since the Reformation was as much about rebelling against abuses by the Church (See several of the points, including but not limited to  #10, 24, 27... here) as it was about differences in doctrine, you might be able to argue that the widespread existence of protestant denominations is at least partially due to the Inquisition.  Certainly, Church-sponsored torture and murder of those who simply believe differently are examples of corruption and abuse of power. If not a direct cause, the Inquisitions certainly would have added fuel to the fire.