The highest scoring cribbage hand you can get is worth 29 points. It consists of a Jack and three fives. The cut card is the five of the same suit as the Jack. So, there are actually four different hands that are worth 29 (each suit). Even so, your odds of getting this "perfect hand" is only 1 in 216,580!
Any ten or face card other than a suited Jack will also give you an impressive 28 points. There are 76 possible hands in which that happens, so your odds are slightly higher, though still extremely slim.
The allure of the perfect 29 hand is so great that many people have it depicted on custom cribbage boards like this one:
Now, go play a game of cribbage and see how long it takes you to get your own 29 hand!