Binomials, or binomial expressions, are frequently used by native speakers of English. The word order of a binomial pair is usually fixed, and to use them in a different order would sound strange to a native speaker.
Here are some common binomials:

Aches and pains Minor pains and a feeling of discomfort, especially in the muscles. After a hectic outing with the kids I had aches and pains all over!
Back and forth Going to and from a place. He's tired of travelling back and forth to London.
Bits and pieces Small items or personal belongings. Here's a cupboard where you can put all your bits and pieces.
Bit by bit Gradually; little by little; a small amount at a time. They renovated the old house bit by bit.
Black and blue Sore and bruised The boy was black and blue after falling off his bike.
Born and bred Be born and grow up in a particular place. I was born and bred in Madrid.
By and large On the whole, generally. He can be difficult but by and large he's a good kid.
Cloak and dagger Refers to stories or situations that involve intrigue, secrecy, espionage or mystery. My young brother loves cloak-and dagger spy novels.
Cut and dried  Clear and definite or unchangeable. There is no cut-and-dried solution to the problem.
Do's and don'ts A set of basic rules. There's a list of Dos and Don'ts on the wall for everyone who uses the kitchen.
Done and dusted Completely finished. We've finished the project. It's all done and dusted, so let's go and get a bite to eat!
Far and wide Over a large area. People came from far and wide to visit the exhibition.
First and foremost What is most important. She went into politics for a while, but first and foremost she was a writer.
Give or take More or less; plus or minus an amount or number. I'll be there at 9 a.m. give or take 5 minutes.
Heart and soul Make a lot of effort to do something. Paul put his heart and soul into the project. Let's hope it will be a success.
Hustle and bustle Noisy activity and surroundings. John moved to a small village to get away from the hustle and bustle of the city.
Ins and outs The finer details of something. I heard he was arrested but I don't know the ins and outs of the story. 
Leaps and bounds Very quickly and greatly. Silvia's English has improved in leaps and bounds this year.
Loud and clear Easy to understand. The announcement was loud and clear; everyone understood.
Neat and tidy With everything in good order. I don't know how you manage to keep your desk so neat and tidy.
Null and void Have no legal force or be invalid. The agreement was declared null and void.

Odds and ends Various small items.
Small tasks to finish.
Part of the garage was full of odds and ends.
I've got to take care of a few odds and ends before I leave.
On and off Intermittently; sometimes. I've been suffering from backache on and off this past year.
Part and parcel An integral or essential part of something. Travel is part and parcel of the job.
Peace and quiet Freedom from stress and noise; a period of calm. I just can't concentrate. I need some peace and quiet.
Pick and choose Select only certain things and reject the others. You must obey all  the rules. You can't pick and choose!
Pins and needles A tingling sensation in a part of the body. I lay curled up for so long that I had pins and needles in my legs." 
Prim and proper Formal and socially correct She's too prim and proper to be seen drinking beer!
Pros and cons
The good and bad sides of something; the advantages and disadvantages. Before we decide on anything we should discuss the pros and cons.
Rant and rave Speak loudly and angrily about something. You can rant and rave about the rules but you still have to obey them!
Rough and ready Hastily prepared but sufficient for the purpose. Without formality or refinement. The map of the area was rough and ready, but we found our way.
Rules and regulations Instructions as to what is allowed or forbidden. The rules and regulations in our school are very strict.
Safe and sound Not injured or hurt in any way. After the avalanche all of the skiers were found safe and sound.
Short and sweet Brief but pleasant or appropriate. His introductory speech was short and sweet – which suited everyone!
Sick and tired Annoyed or frustrated with something to the point of weariness. Tom was sick and tired of having to explain the problem over and over again.
Spick and span Very clean and tidy; spotless. They cleaned up after the party and left the place spick and span.
Step by step From one stage to the next. The whole procedure was explained to us step by step.
Toss and turn Move around restlessly in bed because you are unable to sleep. She tossed and turned all night, and woke up feeling exhausted.
Trials and tribulations The difficulties we face in life It's a book about the trials and tribulations of living abroad.
Ups and downs A mixture of both good and bad experiences or events. Anne and Tony have had their ups and downs but they're still together.
Wear and tear Damage that happens gradually over time due to everyday use. After several years of wear and tear we had to buy a new sofa.