Simple

Canada is a rich country.

Simple

Still, it has many poor people.

Compound

Canada is a rich country, but still it has many poor people.

Compound sentences are very natural for English speakers -- small children learn to use them early on to connect their ideas and to avoid pausing (and allowing an adult to interrupt):

Today at school Mr. Moore brought in his pet rabbit, and he showed it to the class, and I got to pet it, and Kate held it, and we coloured pictures of it, and it ate part of my carrot at lunch, and ...

Of course, this is an extreme example, but if you over-use compound sentences in written work, your writing might seem immature.

A compound sentence is most effective when you use it to create a sense of balance or contrast between two (or more) equally-important pieces of information:

Montéal has better clubs, but Toronto has better cinemas.

Special Cases of Compound Sentences

There are two special types of compound sentences which you might want to note. First, rather than joining two simple sentences together, a coordinating conjunction sometimes joins two complex sentences, or one simple sentence and one complex sentence. In this case, the sentence is called a compound-complex sentence:

compound-complex

The package arrived in the morning, but the courier left before I could check the contents.

The second special case involves punctuation. It is possible to join two originally separate sentences into a compound sentence using a semicolon instead of a co-ordinating conjunction:

Sir John A. Macdonald had a serious drinking problem; when sober, however, he could be a formidable foe in the House of Commons.

Usually, a conjunctive adverb like "however" or "consequently" will appear near the beginning of the second part, but it is not required:

The sun rises in the east; it sets in the west.