The Bible addresses worry and anxiety directly in several passages:
Matthew 6:25-34 (KJV)
25 Therefore I say unto you, Take no thought for your life, what ye shall eat, or what ye shall drink; nor yet for your body, what ye shall put on. Is not the life more than meat, and the body than raiment? 26 Behold the fowls of the air: for they sow not, neither do they reap, nor gather into barns; yet your heavenly Father feedeth them. Are ye not much better than they? 27 Which of you by taking thought can add one cubit unto his stature? 33 But seek ye first the kingdom of God, and his righteousness; and all these things shall be added unto you. 34 Take therefore no thought for the morrow: for the morrow shall take thought for the things of itself. Sufficient unto the day is the evil thereof.
Philippians 4:6-7 (KJV)
6 Be careful for nothing; but in every thing by prayer and supplication with thanksgiving let your requests be made known unto God. 7 And the peace of God, which passeth all understanding, shall keep your hearts and minds through Christ Jesus.
1 Peter 5:7 (KJV)
7 Casting all your care upon him; for he careth for you.
Isaiah 41:10 (KJV)
10 Fear thou not; for I am with thee: be not dismayed; for I am thy God: I will strengthen thee; yea, I will help thee; yea, I will uphold thee with the right hand of my righteousness.