Definitions: Carefulness is being attentive to potential danger, error, or harm; caution means almost the same, except it  also means careful forethought to avoid danger or harm; close attention or vigilance to minimize risk.

1. The Devil is waiting for any careless, unguarded moment in order to deal us a harmful blow.

Psalm 39:1 [A careless mouth can cause a load of troubles] I said, I will take heed to my ways, that I sin not with my tongue: I will keep my mouth with a bridle, while the wicked is before me. [See also Psalm 141:3; Proverbs 13:3]
Proverbs 4:26 [Look before you leap!] Ponder the path of thy feet, and let all thy ways be established. [See also 14:15]
Proverbs 26:2 [Many of our troubles are caused by ourselves] As the bird by wandering, as the swallow by flying, so the curse causeless shall not come.
Matthew 24:4,24 [In the times in which we are living it is important to pray for discernment and wisdom] And Jesus answered and said unto them, Take heed that no man deceive you. 24 For there shall arise false Christs, and false prophets, and shall shew great signs and wonders; insomuch that, if it were possible, they shall deceive the very elect.
1 Corinthians 9:27 [While preaching to others, Lord help us to keep ourselves in check] But I keep under my body, and bring it into subjection: lest that by any means, when I have preached to others, I myself should be a castaway. [See also Proverbs 4:23]
1 Corinthians 10:12 [Self-confidence is dangerous] Wherefore let him that thinketh he standeth take heed lest he fall.
1 Peter 5:8,9 Be sober, be vigilant; because your adversary the Devil, as a roaring lion, walketh about, seeking whom he may devour: 9 Whom resist stedfast in the faith, knowing that the same afflictions are accomplished in your brethren that are in the world.

2. The Lord has promised to protect and keep us, but He  also expects us to do our part.

Proverbs 3:21b,23 [Being careful and cautious means exercising wisdom] Keep sound wisdom and discretion: … 23 Then shalt thou walk in thy way safely, and thy foot shall not stumble.
Proverbs 4:20-27 My son, attend to my words; incline thine ear unto my sayings. 21 Let them not depart from thine eyes; keep them in the midst of thine heart. 22 For they are life unto those that find them, and health to all their flesh. 23 Keep thy heart with all diligence; for out of it are the issues of life. 24 Put away from thee a froward mouth, and perverse lips put far from thee. 25 Let thine eyes look right on, and let thine eyelids look straight before thee. 26 Ponder the path of thy feet, and let all thy ways be established. 27 Turn not to the right hand nor to the left: remove thy foot from evil.
Proverbs 22:3 [Being careful means being watchful and on guard] A prudent man foreseeth the evil, and hideth himself: but the simple pass on, and are punished.
Matthew 4:5-7 [Being careful means not tempting the Lord by being careless or reckless or taking unnecessary risks] Then the Devil taketh Him [Jesus] up into the holy city, and setteth Him on a pinnacle of the temple, 6 And saith unto Him, If Thou be the Son of God, cast Thyself down: for it is written, He shall give His angels charge concerning Thee: and in their hands they shall bear Thee up, lest at any time Thou dash Thy foot against a stone. 7 Jesus said unto him, It is written again, Thou shalt not tempt the Lord thy God.

3. Prayerfulness plus carefulness equals protection and blessing.

Proverbs 3:6,26 In all thy ways acknowledge Him, and He shall direct thy paths. … 26 For the Lord shall be thy confidence, and shall keep thy foot from being taken.
Matthew 26:41 Watch and pray, that ye enter not into temptation: the spirit indeed is willing, but the flesh is weak.
Luke 18:1 And He spake a parable unto them to this end, that men ought always to pray, and not to faint.
Ephesians 6:18 [You should be] praying always with all prayer and supplication in the Spirit, and watching thereunto with all perseverance and supplication for all saints.
Colossians 4:2 Continue in prayer, and watch in the same with thanksgiving.
1 Thessalonians 5:17 Pray without ceasing.
4. Constant vigilance is the price of security.
Matthew 24:43 But know this, that if the goodman of the house had known in what watch the thief would come, he would have watched, and would not have suffered his house to be broken up.
Luke 21:36 Watch ye therefore, and pray always, that ye may be accounted worthy to escape all these things that shall come to pass, and to stand before the Son of man.

5. Here are a few sobering warnings from the Bible regarding the possible results of carelessness:

1 Kings 3:19 [Loss of life:] And this woman’s child died in the night; because she overlaid it.
2 Kings 4:18-20 [Another child whose death resulted from carelessness, this time by sunstroke, was later miraculously raised to life] And when the child was grown, it fell on a day, that he went out to his father to the reapers. 19 And he said unto his father, My head, my head. And he said to a lad, Carry him to his mother. 20 And when he had taken him, and brought him to his mother, he sat on her knees till noon, and then died. [See also 2 Kings 4:18-37]
2 King 6:4b,5 [Loss or damage of property:] And when they came to Jordan, they cut down wood. 5 But as one was felling a beam, the axe head fell into the water: and he cried, and said, Alas, master! For it was borrowed. [See also 2 Kings 6:1-7]
2 Samuel 4:4 [Injury:] And Jonathan, Saul’s son, had a son that was lame of his feet. He was five years old when the tidings came of Saul and Jonathan out of Jezreel, and his nurse took him up, and fled: and it came to pass, as she made haste to flee, that he fell, and became lame. And his name was Mephibosheth.
Matthew 7:26,27 [Foolish disregard to the Word is the most dangerous kind of carelessness] And every one that heareth these sayings of Mine, and doeth them not, shall be likened unto a foolish man, which built his house upon the sand: 27 And the rain descended, and the floods came, and the winds blew, and beat upon that house; and it fell: and great was the fall of it.

6. Lord help us to keep on guard and warn others!

Ezekiel 3:17 [Our ministry is to be faithful watchmen to warn both the righteous and the wicked:] Son of man, I have made thee a watchman unto the house of Israel: therefore hear the word at My mouth, and give them warning from Me. [See verses  18-21]
Isaiah 56:10 [Don’t be like the unprepared, whose] watchmen are blind: they are all ignorant, they are all dumb dogs, they cannot bark; sleeping, lying down, loving to slumber.
Luke 6:39 [Jesus portrayed the Pharisees as blind leaders] And He spake a parable unto them, Can the blind lead the blind? Shall they not both fall into the ditch?
Exodus 23:13a And in all things that I [God] have said unto you be circumspect [aware of circumstances].
Matthew 26:40,41 [The Enemy often strikes when we are tired and weary] And He cometh unto the disciples, and findeth them asleep, and saith unto Peter, What, could ye not watch with He one hour? 41 Watch and pray, that ye enter not into temptation: the spirit indeed is willing, but the flesh is weak.
Mark 13:37 And what I [Jesus] say unto you I say unto all, Watch.
Romans 13:11 [The Enemy is trying to lull God’s children to sleep, to get them off guard] And that, knowing the time, that now it is high time to awake out of sleep: for now is our Salvation nearer than when we believed.
Ephesians 5:15,16 See then that ye walk circumspectly, not as fools, but as wise. 16 Redeeming the time, because the days are evil.
1 Thessalonians 5:5-8a Ye are all the children of light, and the children of the day: we are not of the night, nor of darkness. 6 Therefore let us not sleep, as do others; but let us watch and be sober. 7 For they that sleep sleep in the night; and they that be drunken are drunken in the night. 8a But let us, who are of the day, be sober. …
2 Timothy 4:5 But watch thou in all things. … [See also Revelation 16:15]
Hebrews 2:1 Therefore we ought to give the more earnest heed to the things which we have heard, lest at any time we should let them slip.
1 Peter 1:13 Wherefore gird up the loins of your mind, be sober, and hope to the end for the grace that is to be brought unto you at the Revelation of Jesus Christ. [See also 4:7]