Curious - is that mostly due to character-concept reasons or mechanical/optimization reasons?
Character concept mostly. Usually to make something work for my character idea that I can't get on a single class.
I have never played any of the "power builds" - Sorcadin or Hexadin, although I have played a Shadow Sorcerer/Undying Warlock once.
Usually it is Wizard-Cleric, Wizard-Sorcerer, Wizard-Warlock, Rogue-Anything, Fighter-Ranger, Ranger-Bard, Cleric-Warlock
Multiclassing just gives you a lot more options - healing magic and offensive magic ..... martial weapons and sneak attack ..... armor and spells .....
For example, I have a Goblin Enchantment Wizard I am going to be playing soon in the upcoming Phandelver adventure. She is primarily going to be an Enchantment Wizard, and that is what I want to play, but the character idea is she is going to start the game pretending to be a Gnome Cleric of Tymora and working for a Harper (Sister Gaela) who is a real Cleric of Tymora in Phandalin.
To make this work I am taking the Secret Identity background and I have not decided whether she is going to start as a Trickery Cleric of Leira or a Divine Soul Sorcerer blessed by Leira. Either way she will get the Disguise Self spell, along with disguise kit from her background and some cleric cantrips and spells from her starting class to be able to fool the Harper and towsfolk. We are a couple months away from this campaign so I have some time to figure it out. A straight Wizard would be more powerful and the Cleric mutliclass is the stronger multiclass build, but I will probably end up doing the Divine Soul because I actually like that a bit better thematically and is not as MAD (I will need Charisma for deception regardless, if I go cleric I need a 13 Wisdom too).
A second example - I plan on playing a Damphir Long Death Monk in a Spelljammer campaign. She was a spelljammer and her ship was taken by Vampirates hundreds of years ago. She was bitten and taken prisoner for a few days before being made to "walk the plank" in wildspace. She walked the Plank and driftend away but did not die because her transformation started and she did not need to breath. She drifted for hundreds of years before coming up on a dead god floating. She started to worship the dead God and finally was picked up by a passing ship. So she is going to start as a Death Cleric but then multiclass to Monk.
I have played in highly-optimized games, but that works best if the entire table is doing it and is very experienced. If I was going for optimization I would pick a simpler backstory that would not require as much.