While multiclassing is not explicitly discouraged, the more powerful techniques and abilities available to a class are usually reserved for the highest class levels; taking a level in a new class, or increasing the level of a less-learned class, could result in a character that is effectively a level "behind" the rest of the party.
That being said, some play-styles are only possible, or at least easier, with multiclassing. For instance, Bards and Rogues have techniques for befuddling enemies and moving swiftly around a battlefield. A standard Fighter that wants to be more dynamic in a fight might find it to their advantage to take a level or two in one of those classes.
In the end, whether or not multiclassing can be considered "worth it" depends on the kind of campaign being run, the enemies and scenarios encountered, the composition of the party, and more. Ultimately though, the most important thing to consider is what kind of character you want to play. Maybe you'd rather be a Jack-of-all-Trades skillmonkey who can do a little bit of everything? Or maybe you'd rather be a living hammer, exceptionally good at one specific thing. As long as your Game Master agrees, and you don't cause your teammates any grief, then the choice to multiclass or not is a personal one.