Learn Turkish: Geçmiş önemli değil, bugünkü deneyim önemli. - The past is not important, today's experience is important.

The suffix is almost always -ki and usually doesn't follow vowel harmony. However, words like bugün (today), dün (yesterday), and gün (day) are exceptions. Because they contain the rounded vowels ü or u, the suffix changes to -kü to make pronunciation easier, giving us bugünkü (today's).

If bugünkü means 'today's', why doesn't deneyim (experience) have a possessive suffix?

The suffix -ki turns a time word into a regular adjective. Because bugünkü is now an adjective describing the noun, they don't form a possessive noun compound. Just like you would say güzel deneyim (beautiful experience) without extra suffixes, you simply say bugünkü deneyim.

The word geçmiş looks like a verb with the -miş past tense. How is it being used here?

You are right that it comes from the verb geçmek (to pass) with the -miş suffix attached. Over time, it became a permanent noun meaning 'the past' (literally 'that which has passed'). Here, it acts as the subject of the first clause: 'The past is not important.'

There is no verb like 'is' at the end of bugünkü deneyim önemli. Is a word missing?