CONJUNCTIONS

BUT
      It's very strange, but I like it
 
(AL)THOUGH
      Although/though it's very strange, I like it
This connector may be emphasized by putting "even" before: EVEN THOUGH
     Even though it's very strange, I like it

ALTHOUGH and THOUGH mean exactly the same and are used the same, but THOUGH is more informal and more common when talking, and ALTHOUGH is more formal and more common when writing. Notice that (AL)THOUGH and BUT are both conjunctions and mean the same, but they go with different sentences:

A but B  (BUT can never go at the beginning of the sentence)
B although A / Although B, A

PREPOSITIONS

IN SPITE OF  (followed by a noun phrase or -ing)
      She's sleeping like a log in spite of the noise
      He was elected president in spite of his young age
 
If we want a sentence with a verb then we can’t use the preposition "in spite of", we need a conjunction like "(al)though".
      Although he is very young, he was elected president

But we can use IN SPITE OF + ING (because -ing can be the noun-form of a verb)
      In spite of loving her, he thought it was best to leave
      We didn't want to buy the house in spite of having enough money

Compare:
He stayed in bed in spite of feeling better (in spite of + ing)
He stayed in bed although he felt better (although + subject + verb)

FREE CONNECTORS

The same idea as ALTHOUGH, but as a free connector, can be expressed with these 6 connectors:

ON THE OTHER HAND
      It's not a very nice flat. On the other hand, it's very cheap
      I wanted to go, but on the other hand, I was too tired, so I stayed at home
Optionally, you can use it with ON THE ONE HAND with the other contrasting idea. This dual construction emphasizes the contrast:
      On the one hand I wanted to go, but on the other hand, I was too tired

NEVERTHELESS
HOWEVER
YET / STILL*
THOUGH
ANYWAY
 
They all have the same meaning, but they differ in the place they take inside the sentence:
 
BETWEEN TWO SENTENCES   Nevertheless, However, On the other hand, Yet, Still
      He says he needs money. XXX, he has 2 houses and 2 cars
 
IN THE MIDDLE OF A COMPOUND SENTENCE   Nevertheless, However, On the other hand, Though
      I was getting bored at the party. When she arrived, XXX, I knew it would be fun
 
AT THE END Though, Anyway       (but never "although")
      It's a bit strange. I like it, XXX
 
None of these can go at the beginning of a sentence

* YET and STILL can be adverbs of time (used in just one sentence: click here for more information) or free connectors (used with two sentences)
1 sentence (adverbs):
- I haven't finished yet
- She's still looking for a job
2 sentences (connectors)
- I love you. Yet, I can't marry you
- That's very nice. Still, I prefer the other one
Compare:
- I don't have money yet (but I probably will)
- I like that car. Yet, I don't have money (so I can't buy it) /yet = nevertheless/

For Spanish Speakers

BUT (c) = pero
(AL)THOUGH (c) = aunque, a pesar de que
IN SPITE OF (p) = a pesar de    (seguido de un sintagma nominal o -ing)
 
NEVERTHELESS (fc) = Sin embargo, de todas formas,
HOWEVER (fc) = Sin embargo, de todas formas,
YET / STILL (fc) = Sin embargo, de todas formas,
THOUGH (fc) = Sin embargo, de todas formas,
ANYWAY (fc) = Sin embargo, de todas formas,

ON THE OTHER HAND  (fc) = por otra parte, por otro lado (pero expresando contraste)
- Me gusta Holanda. Por otra parte, hace demasiado frío para vivir allí = I like the Netherlands. On the other hand, it's too cold to live there
- Necesitamos más dinero. Por otra parte, también necesitamos más ideas = We need more money. Besides, we also need more ideas.  (BESIDES= además)
En el segundo caso no hay contraste ni contradicción aparente, sino solamente cambio de tema o extensión del tema, así que ese segundo uso español no se corresponde con el inglés ON THE OTHER HAND, que siempre expresa contradicción (así que mucho cuidado porque los hablantes de español a menudo meten la pata aquí)

YET/STILL (fc)= Sin embargo
No confundamos estos conectores con los adverbios de tiempo, el lugar que ocupan en la frase es diferente y su significado y función es totalmente distinta:
UNA frase: adverbio
- I haven't finished yet = todavía no he terminado (yet va al final)
- She's still watching the TV = todavía está viendo la tele (still va delante de los verbos normales y detrás de los especiales)
DOS frases: free connector
+ I'm reading this book. Yet, I don't like it much = estoy leyendo este libro. Sin embargo, no me gusta mucho
+ I'd like to go with you. Still, I must stay and help my mother = me gustaría acompañarte. Sin embargo me tengo que quedar a ayudar a mi madre