Tends to be poetically used rather than day-to-day. It is still used, but usually in literature such as poetry, set phrases rather than on its own (like 今日晚间), or written documents and names (such as 今日新闻). It's used, but it's really not the most common choice of word for people on the mainland.
The most common; used in regular speech in modern Mandarin.
I've only ever seen this used in Japanese, actually. 本日 is pronounced ほんじつ (honjitsu) in Japanese, and is a formal word for "today", but it's never used in casual speech, only formal occasions such as in business. After a google search, it seems to be used in Chinese sparingly, and matches the pattern of 本年，本月，本日, but I've never seen it used in Chinese before today, only Japanese.
So, in reality I'd say there are only 2 that are actually used, and even of these, 今天 is the only one you really need to be using unless you have a reason not to.