If we want an authoritative source, we could look at the official terminology used by the Japanese government as set out by the Agency of Cultural Affairs (文化庁) (might be familiar name to some people as their page about 二重敬語 gets referenced here sometimes).
They start by saying only to use kanji from 常用漢字表・付表 in the normal form of the character.
They go on to give certain 代名詞 which should be written in kanji,
例 俺、彼、誰、何、僕、私、我々
and 副詞・連体詞 to be written using kanji.
例(副詞) 余り、至って、大いに、恐らく、概して、必ず [...] (long list)
例(連体詞) 明るく、大きな、来る、去る、小さな、我が(国)
They go say 副詞 such as the following in should be written in kana.
例 かなり、ふと、やはり、よほど
They prescribe writing 御 in kanji when the word it is attached it is in kanji, and kana when the word is in kana.
御案内、御挨拶 vs. ごもっとも
and they give the following 接尾語 to be written in kana.
げ(惜しげもなく)、ども(私ども)、ぶる(偉ぶる)、み(弱み)、め(少なめ)
They prescribe writing in kana for 接続詞 such as the following
例 おって、かつ、したがって、ついては、ところが、ところで、また、ゆえに
and kana for the 助動詞・助詞 such as the following
ない(行かない)、ようだ、ぐらい、だけ、ほど
Finally, they prescribe kana for a whole lot of words when used in certain ways (take a look at キ under 1(2)) such as ある・いる expressing existence, the こと in 許可しないことがある, できる such as in だれでも利用ができる, and te-form + verb (てあげる、ていく、ておく、てください、etc etc)
My only problem with all this is: to what extent do prescriptive rules such as these reflect actual usage? Writing te-form + verb in kana seems to generally accepted, as does writing words such as わけ、はず、ようだ、だけ、ほど etc in kana.
However (and here I have a problem with TN's comment) 出来る in kanji is seen all the time in contexts both formal and informal. 従{したが}って, ご案内 (not using 御 as the Agency prescribes), 又{また}, etc are also common.
As this question or this question (see Uberto's answer and Tsuyoshi Ito's comment) for example show, a writer can make use of the 3 writing systems in Japanese to give different impressions (オススメ vs お勧め, ありがとうございます vs 有難う御座います). Some of these will only be appropriate to casual writing, sometimes you will have a choice even in formal writing. This is one of the most fun/interesting parts of Japanese, though I don't know how one could comprehensively describe it...