I have seen many people, particularly LDS apologists, criticize the desire for proof in addition to faith. They say that its not true faith if you want proof, or a "sign," or they'll say that people should just be happy with their beliefs and leave science out of it.
I would say that what it comes down to is that reality and beliefs should match up acceptably, or else its likely that its the beliefs that are wrong. After all, if God is the source of Truth, then he is the source of all truth, and that includes science and logic.
This does not lessen faith in the least, and often strengthens it. I can research all I want about whether Jesus really lived, whether he really died and then was seen alive again, whether the apostles really lived and taught, whether the places mentioned in the Bible existed, whether the history of the Old Testament matches with reality as much as can be verified for such an ancient source, etc. In the end, however, none of that research will tell me whether Jesus really is my Savior and my God. I can only believe that on faith, and that is the faith Jesus asks for.
People who want evidence are not generally condemned in the Bible, with a few exceptions, usually regarding the Pharisees and teachers of the Law, who had the scriptures in their hands and the miracles before their eyes and still doubted. Yet even they received the sign of the resurrection. The Old Testament talks about miracles being performed for Israel again and again. After Jesus left the earth, the earliest believers had the testimonies of multiple eyewitnesses to the life, death, and resurrection of Jesus, including from people who were skeptics or even outright persecutors until after they saw the risen Lord for themselves. Today, we can see much evidence in archaeology and history. I don't think God gave us all this just to condemn those whose faith was strengthened by it, or those who began to have faith because they examined the evidence.
1 Thessalonians 5:21 Prove all things; hold fast that which is good.
Acts 17:10-12 And the brethren immediately sent away Paul and Silas by night unto Berea: who coming thither went into the synagogue of the Jews. These were more noble than... those in Thessalonica, in that they received the word with all readiness of mind, and searched the scriptures daily, whether those things were so. Therefore many of them believed; also of honourable women which were Greeks, and of men, not a few.
Then the question becomes: what if your faith doesn't have evidence? Or worse, has evidence against it? Isn't that called blind faith? Can that not lead to being deceived? Are feelings alone proof, especially if reality contradicts those feelings? We see so many stories of people who have blind faith and who stake their very lives on it, and although their faith is sincere, they are sincerely wrong. So perhaps you should ask yourself some important questions, such as:
Am I comfortable enough with seeking truth to question the veracity of the truth I hold to?
Do I believe that questioning truth will not change what truth is, only possibly what I hold to be true?
Does my faith have any solid support? (archaeology, logic, science, etc)
Does my faith have any proof strongly opposing it? (scientific evidence, forgeries, questionable practices, etc)
If I believe in the Bible, does the Bible support my beliefs, and am I willing to find that out if I don't know?
I remember, when I was Mormon, I believed that if the church was true, it could stand up to questioning. When I finally asked the right questions (beginning with: Was Joseph Smith a true prophet?), the church did not stand up, and I left.
I have done research on the veracity of Christianity, and continue to do research. I am taking it one step at a time: as a new Christian, I don't want to overload myself with the views of critics, I want to be able to take it one step at a time and consider each thing I learn. If I were to learn something that disproved Christianity to me as thoroughly as Mormonism was disproved to me, I would leave it. If it is not truth, I do not wish to believe it. However, Christianity has so far stood up to the test and to my questions. Though I will not stop researching, I believe Christianity will continue to stand up to the test. The difference between Christianity and Mormonism is that I am not discouraged from reading and researching what skeptics and atheists have to say about it, because if Christianity is true, it will stand up to those tests.
The more I research Christianity, the more I am amazed. I am amazed at the reality of the life, death, and resurrection of Christ as recorded in history, even extra-Biblically. I am amazed at the amount of prophecies Jesus fulfilled and the sheer improbability (almost impossibility) that he would do so--fulfilling just eight was so unlikely, that there are less atoms in the universe that the one in whatever chance that he would do so. I am amazed that I can walk where he walked. I am amazed about who he claimed to be, and at his ability to prove it--other religious teachers and prophets like Buddha and Muhammad never claimed to be God, because they could in no way prove that they were. I am amazed at the improbability of this universe existing perfectly how it does.
All of this does nothing more than support my faith, and I am grateful to see the sheer brilliance of the work of God in proving himself to us. But in the end, my faith is in Jesus Christ, my Lord, my Savior, and my God.