Tim Bowen provides us with an even balance of the varied uses of this word.
Even is one of those nasty English words with more than one word class. It can be an adjective – an even surface, an even number, an even balance, an even temperature – or it can be a verb – to even the score (although, as a verb, it is more commonly used with the particle out).
Even can also be an adverb and here it has three main uses. First, it is used for showing that you are saying something that is surprising, e.g. Even the dog refused to eat it or It’s always cold in this room, even in summer. It is used in a similar way with now and then, as in Even now, after all these years, he cannot mention her name without crying or He’s getting a tax rebate and even then he won’t be satisfied, and with not, as in They didn't even offer me a cup of tea.
Even is used before verbs (She even forgot my birthday) but after auxiliary verbs and modals (He can’t even spell his own name!). Its second use is with comparatives and is used to emphasize that although something is big, good, bad etc, something else is bigger, better, worse, etc. (e.g. Local people are treated even more harshly than foreigners or Things were even worse under the previous government).
The third use of even is to add a more extreme word or phrase to emphasize what you have just said and may be used in different positions for extra emphasis, e.g. His latest film is very good, even brilliant or His latest film is very good – brilliant, even.