One of the verses I often go back to in life is Psalm 55:22 which says, "Cast your burden upon the Lord and He will sustain you; He will never allow the righteous to be shaken." John Piper gives a good exhortation on this verse:
The word for "burden" here is "lot." What is your lot in life today? What has providence brought you? This is finally of the Lord. And he will carry it for you. It is not meant to crush you or carry you away. It is meant to test your trust in God to carry it for you. (See also Psa. 16:5; 63:8.)
Here's a little song (written by the folks from Seeds) that captures this truth of God carrying our burdens. It's written for children and for all those who would become like children trusting in their Father's love. Thanks to Kellie Shramek for pointing me to this video!