Contrasting ideas

But contrasts two ideas in the same sentence.
http://www.wordreference.com/es/translation.asp?tranword=but
The weather was bad but she enjoyed the trip.

Although and though (informal) are also used to contrast ideas in the same sentence. They can go at the beginning of a sentence or in the middle.
http://www.wordreference.com/es/translation.asp?tranword=although
http://www.wordreference.com/es/translation.asp?tranword=though
Although the weather was bad, she enjoyed the trip.

However contrasts ideas in two different sentences. It often comes at the beginning of the second sentence and is followed by a comma.
http://www.wordreference.com/es/translation.asp?tranword=however
The weather was bad. However, she enjoyed the trip.

Nevertheless is a more formal alternative to however.
http://www.wordreference.com/es/translation.asp?tranword=nevertheless
The English aren't normally very emotional people. Nevertheless, they get very excited at sporting events.

In spite of and despite are both followed by a gerund or a noun. They can go at the beginning of the sentence or in the middle.
http://www.wordreference.com/es/translation.asp?tranword=in%20spite%20of
http://www.wordreference.com/es/translation.asp?tranword=despite
Despite the fact that the weather was bad, she enjoyed the trip.
If the subject of the verbs in the two clauses is the same, the gerund can be used immediately after despite or in spite of without a preceding noun/pronoun.
She played tennis despite feeling ill.

Whereas and while are used to contrast two ideas in the same sentence.
http://www.wordreference.com/es/translation.asp?tranword=whereas
http://www.wordreference.com/es/translation.asp?tranword=while
The first photo shows a child having fun whereas/while the second one shows a rather sad man on his own.