"Which of you by taking thought can add one cubit unto his stature?" Matthew 6:27 (KJV)
"And which of you by being anxious can add a single hour to his span of life?" Matthew 6:27 (ESV)
Our group has been memorizing this passage in KJV and ESV, and in this verse we come to the only place in our passage where the two disagree, and even then they only partly disagree. The ESV actually includes a footnote that says "Or a single cubit to his stature". The tradition of letting the English reader know when there are other possibilities is a one that goes all the way back to the 1611 KJV, but nevertheless in our primary translations these two passages disagree slightly so let's see why.
On rare occasions differences between translations will be because there is a difference in the Greek originals, but that is not the case here. The Greek is undisputed (it is: τίς δὲ ἐξ ὑμῶν μεριμνῶν δύναται προσθεῖναι ἐπὶ τὴν ἡλικίαν αὐτοῦ πῆχυν ἕνα, if you really wanted to know). So why the different translations?
One free online resource that can be a help explaining why these types of differences exist is the New English Translation (or NET Bible). This Bible gives explanations of why the translators made the choices they did, and their explanations are often helpful in understanding why there are differences among translations. Although the NET can be pretty technical, you can often get a general idea of what is going on even if you don't know the jargon. For this verse, the NET has this note:
"Or “one cubit to his height.” A cubit (πῆχυς, pēchus) can measure length (normally about 45 cm or 18 inches) or time (a small unit, “hour” is usually used [BDAG 812 s.v.] although “day” has been suggested [L&N 67.151])..."
In other words, there is debate about what the Greek word for "cubit" means. One well known Greek dictionary (BDAG is an abbreviation for the last names of the authors who worked on this dictionary) thinks the word means "hour" while another dictionary (L&N, also the abbreviation for the authors) thinks the word means "day."
"...The term ἡλικία (hēlikia) is ambiguous in the same way as πῆχυς (pēchus). Most scholars take the term ἡλικία (hēlikia) to describe age or length of life here, although a few refer it to bodily stature (see BDAG 435-36 s.v. 1.a for discussion)..."
So the Greek word ἡλικία (hēlikia) means length, however, many scholars think that length in this context is referring specifically to length of life. Some, however, disagree and think the plain meaning of the word refers to a person's height. So we have two words here in the Greek that could take this passage in two slightly different directions. How do we choose? Why did NET choose what they chose?
"...Worry about length of life seems a more natural figure than worry about height. However, the point either way is clear: Worrying adds nothing to life span or height."
Other than junior high boys wanting to be able to dunk, few people spend much time worrying about their height, at least enough to try and change it. Because of this the translators of the NET went with long life, because people do spend a lot of time trying to lengthen their life, often to little avail. It could be argued, however, that this is exactly Christ's point. Trying to change the future by worrying is as silly as trying to change your height by worrying. You won't get very far. Because Christ is talking in context about meeting the necessities of life, I lean toward the first. But I can see a argument being made either way.
However you read it, the point of this passage is clear and we don't want to miss the forest for the trees! Your worry doesn't actually solve your problems. You can't make yourself taller, and you can't make yourself live longer. Rather than frantically trying to figure out how we will make it in life, Jesus calls on us to have a firm, calm trust in our lovingly heavenly Father. Understanding the point of this illustration isn't hard. Actually living it out is.