Although the phrases in this column are in no particular order. This is perhaps the mistake I hear the most.
It is so common that even advanced level students make it.
 

In English we go to a place. 場所に行きます
○ Go to Tokyo  東京に行きます
○ Go to the Cinema 映画館に行きます
 

Shopping is not a place. It is a verb (to shop), so some examples are:
○ I go to the supermarket.
○ I go to the department store.
○ I go shopping every Sunday.  
○ I went shopping at the mall.
 

In English we say department store not ‘depart.’
Depart is a formal way of saying leave.（デパートは和製英語です。ご注意ください）
Go to shopping is a direct translation from 買い物に行きます, but it is not used in English.
 

Shopping can be a noun. For example;
○ I brought the shopping home. 買った物を家に持って帰った。
But we would never say  
× I go to the shopping.
This would mean; 私の買った物がある場所に行きます。

Here is another common mistake similar to #1.
 

Home is sometimes a noun. For example;
○ My home is bigger than your home. 私の家はあなたの家より大きいです。
In this example Home is similar to house. But home has a more personal feeling to it. A house is just the building. A home is where you live and feel comfortable, often where your family live too.
 

The mistake here is that home is also an adverb.
So when we use the verb go, we don't need to because we are not talking about a place.
 

The correct sentence(s) should be;
○ I go home. 家に帰ります。
○ I went home. 家に帰りました。
○ I got home at 10 oclock. 10時に家に着きました。
(get home means to arrive home.)
 

Using #1 we can say
○ I went to your home last night.  昨夜あなたの家に行きました。
Your home is a noun (a place), not an adverb, so we can use to. Using only home means it is an adverb,
so we can't use to.
 

Call is another verb that we (usually) don’t use a preposition with.
 

If we want to use a telephone, we say;
○ I called my friend last night (on the phone.)
○ I call my wife every day.
○ Don't call me again!
× He called to me on the phone. Call to somebody, usually means to shout to them.  
 

For example they are across the street.
○ I called to him but he didn't hear me.
 

We don’t use the word to with visit.
 

The correct sentence should be;
○ I will visit Tokyo next week.
○ I will go to Tokyo next week.
 

Here we have a bad translation from the Japanese, where we use counters (枚、 個、 本 etc,)  So a direct translation would indeed be 5 pieces.
 

However pieces in English (usually) refers to a small part of something bigger. If we were to drop a plate, it would break into many pieces.
There would be many pieces of (one) plate.
 

The same would be for;
○ A piece of cake. (A part of a bigger cake.)
○ A piece of plastic. (An unidentified part of a bigger object.)
 

Sometimes it is a little less clear what the bigger thing is.
○ A piece of paper. (Sometimes part of a bigger notebook/ pad of paper.)
○ A chess piece. (Usually part of a set of pieces.)
△ I have seven papers.
○ I have seven pieces of paper.
 

To go back to our original sentence, it should be just;
○ I smoke five cigarettes every day. 毎日タバコを５本吸っています。
○ I have five CDs. CDを５枚持っています。
○ My company sold 10,000 gearboxes last year. 私の会社は昨年ギアボックスを１万個を売りました。