Part of the reason they switch to super deformed style is so that they can save money on animation. Its faster and therefore cheaper to animate with less details. Sometimes they do it for comedic effect, which usually works. Sometimes its to convey something, such as a character's emotions. Anime cannot convey the same subtlety in character emotions that live action film can, so the animators have to exaggerate it to communicate the point.

Now, as for shows that do not often use this technique, it depends on your particular tastes. Here is what I like, maybe something will pique your interest:

Heaven's Lost Property (this one actually uses a super deformed style semi-often, but I still liked it so I am listing it here anyways)

Chobits

Black Lagoon

Full Metal Panic!

Neon Genesis Evangelion

Bubblegum Crisis (NOT Tokyo 2040)

Bubblegum Crash!

YU-NO (the iriginal game is literally a masterpiece, too bad the remake butchered the art style and soundtrack balancing becauae I like the removal of certain... "content")

Akira (anime movie widely regarded as the greatest anime film of all time, not seeing it is actually committing a crime)

Super Dimension Fortress Macross / Robotech (Robotech version is slightly altered, but essentially the same story)

Overlord

Shuffle!

DearS

Konosuba

Record of Lodoss War (the original OVA series)

The Melancholy of Haruhi Suzumiya (yes, I will judge you if you skip the Endless Eight Arc)

Goblin Slayer

DNA^2

Is this a Zombie?

Dallos

Jin Roh: The Wolf Brigade (the original, not the Korean Live Action remake, which was okay but not anime)

Trigun (the original, not the new one -- RIP Millie)

Cowboy Bebop

Parasite Dolls

AD Police Files

Angel Beats

Samurai Troopers

Dirty Pair

Chaika The Coffin Princess

Spice and Wolf

Kill la Kill (this one changes art style a lot, but thats a Studio Trigger signature, not the same as super deformed)

Shenmue the Animation (pretty accurate telling of the first two games, but the pacing is pretty wuick compared to the game, watch this only if you dont want to play the game)

takt op.Destiny

Captain Harlock

Darling in the Franxx

Is it wrong to pick up girls in a dungeon?

Charlotte

Classroom of the Elite

Arifureta

Shimoneta

Knights & Magic

Pumpkin Scissors

The Quintessential Quintuplets

Ghost in the Shell