A classic scenario in D&D is when a player has been kidnapped and replaced by doppleganger. It's a narrative tool to force splitting the party or to place the party in a location in the narrative. Maybe you use these to kidnap an NPC important to the party, giving the enemy an upper hand. Before we start make sure to clean the knapsacks, no one wants to smell those.
Before kidnapping a character you need to formulate a motivation behind the kidnapping. Do they want ransom money? Are they trying to make the party more vulnerable? Do they need information from a character? Is the kidnapper a monster trying to find its next meal? Kidnapping for the sake of kidnapping is not compelling and makes the kidnapped character feel like they are being targeted for no reason.
Deus ex Machina
I'm sure everyone and their cousin has heard the phrase Deus ex machina, but for those who haven't it's Latin for "god from the machine". The use of the term has evolved to refer to a plot device that solves a problem most times one that is unsolvable. It is a tool at the GM's disposal that is a dangerous weapon either for the benefit of the party or for their antagonists.
In short, you can create a scenario in which the character has no escape, the enemy uses a deus ex machina to kidnap that character. This is useful for the GM in the sense that their plan has succeeded and presents the players with a new challenge. By using this plot device you need to make it appear as if you aren't using one, such that the player thinks it was their mistakes that led to their capture. The moment they realize there is nothing they can actually do is when a kidnapping goes from bringing drama and tension to feeling cheated.
The easiest way to hide using a deus ex machina is actually to limit the number of responses that the player has to the kidnapping. For example, you may make the party member taking up the rear in a marching order to make a saving throw. If they failed, maybe they begin to feel sleepy or they get tangled in some webs. This may give them a chance to pull off one more thing before they are whisked away. With each action you give them, you should be taking away more and more of their options. This is why you should limit it to one or two at the most.
In some situations you can get away with giving the players no chance to respond. In these situations you need to then give that player another form of agency. For example, the players are headed through a town when without anyone noticing the party member at the rear or separated gets kidnapped. A doppleganger takes their place and the party proceeds as normal. When this happens you let the player control the doppleganger as if they were their own character. When done in secret this can be an amazing reveal and it gives the player another form of control.
Sometimes you just have to kidnap an NPC, luckily as the DM you have much more control over it. Your only concern should be how your players respond to it, if they have a chance to respond. Since you are capable of controlling if the NPC fails or succeeds you don't need to worry about the NPC getting away because of luck.
Even if you fail to make the kidnapping an engaging experience, you can at least make the act of finding the kidnappers more captivating. Whenever someone is kidnapped have the character drop something, or even the kidnapper drop something. For instance, the player manages to pull out their weapon just as a spider is grabbing them. When they have failed and have been pulled away their weapon falls, leaving behind a web coated sword. This gives anyone trying to find the kidnappee a chance to follow a lead. By not supplying a clue you leave most all of your trails cold and the players even more at the whim of the GM, which sometimes is not an amazing feeling.
More intelligent kidnappers may reach out to other characters to negotiate the release of the kidnappee. This could be counted as another clue but I recommend that you don't let this message be the sole clue. Leave it a bit open ended for how the players want to handle the negotiation. Will they wait in ambush to jump the kidnappers? Will they try to use diplomacy to get the kidnappee back? Maybe your players will be more resourceful and find another way.
Kidnapping characters should be a tool that you use sparingly. When you do so, careful planning can make the scenario a fun distraction from the normal campaign or an addition to your story. With luck you can pull off a kidnapping that will keep players at the edge of their seats.
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