I always wonder whether 'today' and 'tomorrow' should be capitalised. Can anybody help me?
Today and Tomorrow are not capitalized because they are not really names, nor are they proper nouns.
They are capitalized only if they appear at the beginning of a sentence, or if you are making a title for some sort of event such as "The Today News". Otherwise, it is a plain old regular word.
I have written this today and may or may not get an upvote for it tomorrow
The words today and tomorrow are only ever capitalized in titles:
The Today Show (TV program)
Tomorrow Never Knows (Beatles song)
But in everyday speech, these words are left lower-cased:
I'm going to take it easy today. I have a big day tomorrow.
Edit per Christian's comment:
English does not capitalize nouns unless they are so-called proper nouns, by which I do not mean proper in the British sense of being "in order" or "the way a thing should be done," but instead nouns that are used as actual names for people or places or ideas that are represented in titular form. The other variety of nouns are called common nouns, and they refer to everyday things that are not singled out for such special naming. Unlike German, in which every noun is capitalized, common nouns in English are not singled out for special treatment (unless, of course, they come at the beginning of a sentence, or are used as class identifiers in a poetic sense: occasionally you will see truth or beauty written as Truth or Beauty, signifying that these represent special philosophically representative uses of the terms).