That's the question Christ asks about being anxious in today's Gospel from the 1962 Missal.
I'd say the gist of the whole Gospel passage, Luke 12:22-31, is summed up in two verses, 25 &26: "And which of you by being anxious can add one cubit to his span of life? If then you are not able to do as small a thing as that, why are you anxious about the rest?"
In other words, being anxious is good for nothing. This is a message I would personally take to heart as I currently have so much on my plate. It helps to take Christ's questions in the above verses as addressed to one personally; being anxious about things is useless, why do it?
For those of us who may suffer from the habit of worrying, we are offered in the same passage anxiety's counter-virtue: faith; "if God so clothes the grass of the which is alive today and tomorrow is thrown into the oven, how much more will he cloth you, O men of little faith?" (28) A result of weak faith is little trust in God's omnipotence and his initiative to care for us with a love beyond anything we can imagine. We know that the best way to fight vice is not necessarily to extinguish it completely so as to leave a vacuum in our lives where the vice once resided (see Mt 12:43-45, Lk 11:24-26), but to replace the vice with its opposite virtue, so as to flush the vice out and fill that place where the vice formerly dwelt. Let us pray to be "men of much faith" so as to trust in God's almighty power to take care of even the most seemingly complex areas of our lives, and leave little room for worrying.