In Sweden the big-game funding season just ended. April 6th was the deadline for Science Council (Vetenskapsrådet, VR) applications. For most scientists in Sweden this is commensurate to NIH funding for the medical sciences in the US. It is something you can use to introduce yourself and gain instant credibility, as in: "I'm a VR-funded scientist." Implying, of course, that such a scientist is better than the other kind. In this case the other kind often agrees.
When writing a VR application there are three important questions to answer: Why the project? Why you? and, Why at your department?
The first is kind of obvious. If you want money for doing something then you have to show that doing it is interesting, important and not impossible. Avoid double negations though, natural science reviewers value clarity over alliteration.
The second is easy to under-do. 'Aren't my papers enough?' you might ask. The short answer is: no. You have to make sure to cite your own data in the background, your reviewers shouldn't have to look for it. And yes, your previous work should be made to look central to the field, how could you possibly know anything about it? Then, the preliminary data is another large part of the 'why you'-question. It is where you show that what you propose is actually feasible, for you.
The third: 'Why at your department' is sometimes tricky. It is seldom the case that there is only one obvious place for a project to be done. However, it has to be absolutely clear that a given project is possible at the department of the applicant. Make it obvious that the project is suited for your place of work, and tease out something that makes it a really good place for the proposed research.
Foremost in your mind should be that reviewers are subtle and quick to anger. This means that your proposal should formally impeccable; no spelling errors, no fancy punctuation and no awkward alliterations. Further, there should be no claims that runs the risk of not being believed, or claims that has to be checked. The funding asked for should be something that the agency could reward; don't ask for too much, and, just as importantly, don't ask for too little. Finally, be short and to the point. There should be only one aim, and it should be clear as the vitreous humour of a hawk.
Anyway, that's a short summary of the advice I have been given while writing my application these last few weeks. Now I only have to wait six months before the awarded grants are announced in November.