The correct pronunciation of th seems to be one of the bigger challenges for people who want to learn the English language. Apart from the fact that the pronunciation of th varies from word to word, some of the sounds associated with th do not exist in other languages, and may therefore be difficult or uncomfortable for non-native speakers. However, getting the pronunciation right can be a matter of life and death, as hinted at in this video:
How to pronounce th
The th is pronounced in one of three different ways, depending on the word. The three possibilities are:
[θ] (called theta, or voiceless dental fricative; tongue keeps touching upper incisors while air is blown) The theta sound seems to be the hardest sound of the English language for many non-native speakers. It is found in words such as think, theme, through, thrive, or thank. A possible explanation for the reluctance of many German speakers to use the [θ] in English is that this sound is regarded as a speech disorder in German, the so-called Lispeln. However, by doing so, they in fact create a speech disorder in English.
In some words, the th is silent, as in asthma.
Importantly, a given word usually only has one correct pronunciation of th. (I cannot think of an exception right now.) Hence, it is not correct to pronounce the th in the as [θ] (see also here), or to pronounce the th in birthday as [ð] (see this post). Recognizing the fact that th is not always pronounced in the same way is a crucial step toward better pronunciation. A good example I have previously written about is the word birthday, see here.
How not to pronounce th
Non-native speakers often use alternative pronunciations of th. Apart from mixing up the eth and theta sounds, they pronounce th as
[s] Using [s] instead of [θ] makes think sound like sink, think like sing, and truth like truce. Replacing [ð] by [s] gives also instead of although, and say instead of they. Hence, the use of [s] for th is not a good idea.
[f] Pronouncing th as [f] (most often done to avoid the [θ]) also makes you very hard to understand. For example, thus will sound like fuss, there will sound like fair, and bath will sound like barf.
[th] Although quite rare, I have heard people pronounce th simply as t plus h. Since the h will be hard to hear after a t, this will make words such as thank and then sound like tank and ten, respectively. The worst case I came across so far is somebody pronouncing third like turd when talking about third-party funding.
[v] Some people avoid the [ð] in words such as smoothie by pronouncing the th as [v] instead. Creative, but still not correct.
While [s] and [f] may be the sounds most similar to [ð] and [θ] in languages such as German, use of these sounds often confuses native and non-native speakers and should hence be avoided. An rather amusing phenomenon in the (German-speaking) online world is the custom to use fred instead of thread in discussion forums, in order to avoid the th. The th sound even seems to be scary enough for Lenovo to pronounce ThinkPad as [sɪŋkpæd] (Sinkpad) on their phone hotline in Germany. Quite often, the th is also mispronounced in English names such as Samantha, Perth, Bath, or Heathrow. If you are interested, have a look at my previous posts about the words the and thesis.