I have seen this question asked a few times, so here's the best answer I am able to give.
 
 
These HSK 3 example sentences demonstrate the different ways that some HSK 1 words can be used. See my other posts for HSK 1 and HSK 2 example sentences.The first 70 hanzi sentences (to which I added pinyin and English) were taken from the HSK information published by Hanban on www.chinesetest.cn . The rest were created by me to demonstrate the way that specific words (highlighted with 『』square brackets) are used. They are also available as a flashcard text file for HSK levels 1-3. Please share any more examples that you have in the comments. 94 sentences are with hanzi, pinyin, and English are shown after the jump!

 
 
These HSK 2 example sentences demonstrate the different ways that some HSK 2 words can be used. See my other posts for HSK 1 and HSK 3 examples. They are taken from the HSK information published by Hanban on www.chinesetest.cn . They are also available as a flashcard text file for HSK levels 1-3. Please share any more examples that you have in the comments. 53 sentences are with hanzi, pinyin, and English are shown after the jump!

 
 
These HSK 1 example sentences demonstrate the different ways that some HSK 1 words can be used. See my other posts for HSK 2 and HSK 3 examples. They are taken from the HSK information published by Hanban on www.chinesetest.cn . They are also available as a flashcard text file for HSK levels 1-3. Please share any more examples that you have in the comments. 48 sentences are with hanzi, pinyin, and English are shown after the jump!

 
 
As well as learning the vocabulary for each HSK level, you have to learn how to use the words in a sentence. For some words such as nouns this is pretty obvious, but some verbs and other harder to classify words can only really be learned by example. I have created files which give example sentences for HSK levels 1-3, but even if you aren't studying for the HSK they might be useful for you.

You can either browse these files to verify that you understand the usage examples or import them into a flashcard testing app. There are versions formatted for both Pleco and for Hanzi StickyStudy. The formats are simple tab-separated and it shouldn't be hard to modify them for other flashcard programs.  I mentioned this file before, but I have added English translations for level 3, and started adding my own example sentences for a few of the level 3 words where the usage isn't completely obvious.
 
 
I'm a big fan of the AllSet Learning Grammar Wiki, and one of the most useful things I've come across on there is a few pages that list Chinese grammatical points according to their European Common Framework level. These six levels roughly correspond to the six levels of the New HSK, so it would be a good idea for someone studying for the HSK to ensure that they are familiar with all of the grammar points at their level and below. Each list of grammatical points links to a page with more explanations and examples, a really great resource! I have noted the corresponding HSK levels for each page.
 
 
[Update 2nd December 2013: I added links to an HSK-aware dictionary to all the characters below!]

Once you have learned a few hundred Chinese words, you start to come across sentences where you recognise all of the characters but have no idea what the actual meaning of the sentence is. This is because there are many 'patterns' in Chinese where a set arrangement of words has a specific meaning.

Common Chinese Patterns 330 is a fantastic resource for picking up subtle grammar points that are easily missed. This book will help you to improve your grammar at any level, through clear examples. If you are studying for one of the HSK levels 1-5, you may not want to just work through the book from start to finish however, as you will be introduced to patterns that use characters above your level. The hanzi in the chapter list were coloured by HSK level using this script and then grouped by hand. The colours for HSK levels 1-6 are in the order that they appear in a rainbow: red, orange, yellow, green, blue, violet.

The following list splits up the 'chapter' titles (patterns) by HSK level. Note that many of the patterns will not be encountered at the levels shown even though all of the characters are known at that level. In the long run I don't think it hurts to be exposed to these patterns early on though, and reinforce the meanings of the characters and words that make them up.

Another couple of caveats: The example sentences for each pattern ignore HSK levels of course. It would be a good exercise to create some new example sentences for each pattern that only use characters from the HSK level in which it appears - if I get around to doing this I'll share the results (Feel free to send me any sentences that you create). Also some patterns have alternative words, and the alternatives may have different HSK levels. I have grouped these patterns at the higher of the two levels, to save studying the pattern twice.