Which sentence is more correct?
- As everyone I dream about travelling to other countries.
- Like everyone I dream about travelling to other countries.
In this sentence I would use "like".
We generally use LIKE and AS to make comparisons.
LIKE
The structure of the sentence is usually: VERB + LIKE + NOUN / PRONOUN.
He speaks like a native speaker. She looks like a supermodel.
AS
The structure of the sentence is usually: AS + SUBJECT + VERB.
Nobody sings as she does. They went to the party as they were.
It is very common in American English to use LIKE instead of AS. However, it is generally considered informal to use it in this way. We play football like champions do.
Another use of AS is to say what the role/function of a person/thing is. He started work as a carpenter. She used the tapestry as a decoration in her living room.
LIKE vs. AS
Be careful, in similar sentences that use LIKE and AS, the meanings of each sentence are very different. For example: As your boss, I must warn you to be careful. (I am your boss.) Like your boss, I must warn you to be careful. (I am not your boss, but he/she and I have similar attitudes.)
Personally, I prefer like Also, you need a comma.
Like everyone, I dream about travelling to other countries.
Or you could use
As everyone does, I dream about travelling to other countries.
The use of like and as is often confused. like is a preposition whereas as is a conjunction. What you have to do, in practice, is to use like when no verb follows. You can see, in fact, the examples by Michael:
Like everyone, I dream about travelling to other countries.
As everyone does, I dream about travelling to other countries.
In your case, the correct sentence is
Like everyone I dream about travelling to other countries.