The Sopranos is the only show got it right its portrayal of dreams.

[Samtemdo8]

How most stories tackle dreams that we humans experience in our sleep tends to be a bit too "clear" like their not dreams their visions of things to come or metaphors that are clearly obvious.

The Sopranos on the other hand imo, got it right its depiction of dreams, at least some of the Dream sequences. Becuase in real life, Dreams are weird, random, and make no sense. And often times you may or may not be self aware in your dreams.

The show has a lot of dream sequences but my favorite ones are two of Tony Sopranos' dreams.

This one from Season 2 in relation to his descision to whack his friend Pussy Bonpensiero. (Doesn't show the whole Dream sequence, but it gets the point across how random dreams are)

And this one from I think Season 5 I think, in relation to his Cousin Tony Blundetto (again it doesn't show the entire Dream Seqeunce but still:

The best thing about these dreams is that everything "looks normal" like your not in a ridiculous fantasy world were suddenly dragons are flying in new york city or something, but you can tell there is something strange is going on, and when things starts to became completely insane that's when you freak out from it.
And that's what makes these dream sequences the best, because even at times I had dreams like this, where it seems like I'm still in reality, but things are different and at times doesn't make sense.

 

[happyninja42]

Buffy the Vampire Slayer had a few episodes that dealt with dream logic, and they did them very well I thought.

Also they had an episode where Buffy was basically tripping on drugs, and the visuals of that were.....very accurate to my personal experience on LSD.

As to dreams looking "normal", well that's variable, as I've had some very mundane dreams, and then some incredibly bizarre dreams that are straight out of something from a psychedelic Pink Floyd light show. So just because a dream sequence in a show is not "normal" doesn't mean it's less dream accurate. Dreams be weird as shit.

 

[Johnny Novgorod]

I love the dream sequence in season 4 that ends with a shadowy figure at the top of some stairs. It captures how creepy and unsettling a dream can be without being overtly threatening or becoming an obvious nightmare. That's how it works for me, I couldn't separate my dreams from my nightmares. And I like the relative "normality" of Tony's dreams and how they're fed with random people or situations from a day in Tony's life, yet at the service of enacting some deep anxiety.

 

[Casual Shinji]

Probably not the only show, but it's certainly one of the best. I always really liked Christopher's dream about his first kill.