Can anybody recommend some songs which you really get caught up in when you first listen to them?

You mean songs like this?

I'm not exactly sure if this is what you're looking for, but at least for me, these match your description.

Footloose - Kenny Loggins
Total Eclipse Of The Heart - Bonnie Tyler
Hammer To Fall - Queen
I Confess - KD Lang

If these aren't the songs you want, please tell me.

'Bring Me To Life' by Evanescence.

'Pale' by Within Temptation.

Avril Lavigne (anything).

'Rose Coloured Glasses' by Kelly Rowland.

'Teenage Dream' & 'Firework' by Katy Perry.

'Imaginary' by Evanescence.

'Umbrella' & 'Disturbia' by Rhianna

'Told You So' by Carrie Underwood.

'Beautiful' by Christina Aguilera.

'All Night' by Natasha Bendingfield (feat. Jordin Sparks.)

'Wild Horses' by Natasha Bendingfield.

'I Need You' by LeAnne Rimes.

'Linger' by the Cranberries.

'Battlefield' by Jordin Sparks.

'Behind These Hazel Eyes' by Kelly Clarkson.

It's like I'm in a music trance every time I hear this song:

As long as you love me - Backstreet boys

More than that - Backstreet boys

Hello - Richie Lionel

Definitely "Creep" by Radio Head.

Enchanted-Taylor Swift
Dancing Away with my heart-Lady Antabellum
Separate Ways-Journey
Just to name a few :)

should i make a list? here's the order of my list tht it's in. it goes
Disturbed
Lil' Wayne
Eminem
Enigma
Breaking Benjamin
Meat Loaf
TLC
Samantha Lambardy
Evenecence
2Poc
just 2 name a few artists....my current fav. song is 2 Outta 3 Ain't Bad.

This is my favorite song EVER!

Xandria- In love with the Darkness
Xandria-Winterhearted
Evanescence-My Immortal
these are a couple of the ones where I zone out when I'm listening to them

"Ho hey"~ lumineers

Twice by Little Dragon :)

These songs are my fav "zone out/enjoy music" songs:
1) My Song-Girls Dead Monster (Iwasawa ver./from Angel beats/look for eng lyrics vid on Youtube)
2) Keep Holding On-Avril Lavinge
3) Dreams of an Absolution-idk artist (Silver the Hedgehog's theme)
4) Breaking the Habit-Linkin Park
5) If Everyone Cared-Nickleback

I don't know if these are what you are wanting, but...
Hello World - Lady Antebellum
I Won't Give Up - Jason Mraz
Skinny Love - Birdy
Forever Changed - Carrie Underwood

(a joke song:)
Nyan cat

(For real song:)
The Night Santa Went Crazy, Weird Al Yankovich
I Won't Give Up, Davis Mraz
Wide is Your Love, Chris Tomlin

diamonds by rihanna

This one, Simple & Clean, Merry Christmas Mr. Lawrence, Come Back To Me -Utada. Lonely, It Hurts -2NE1. She's a Ghost in the House, My Friend -Miss Emily Brown( most soothing )

what makes you beautiful that song really makes me feel better about myself

ground shake by dirty radio... I get in the zone :)
also beauty and a beat by Justin bieber or n****s in Paris by Jay z and kanye west . the beat of those songs make me go into a different zone :)