It is/was the most exciting trip that I had/have had/had had.
If the trip is not finished use "is" otherwise use "was". And for the second part you should use "had had" unless the sentence is further modified.
Americans sometimes neglect to use present perfect but it's easily the more appropriate tense for this kind of sentence. The connection to the present is that up until this point in his life he has not been on a more exciting trip and just about any time you speak about the entirety of your life in this context you use present perfect.
For example, if you want to express that you have not ever been to a certain city you say "I have never been to that city" (present perfect) and you don't say "I never went to that city" (simple past).
But if you are talking about a specific time frame in the past, and not your entire life you use simple past, e.g. "I was supposed to go to that city last year, but I never did go".
So as a basic rule, when you are talking about your entire life up to this moment you use present perfect tense.
- "I have lived a rich life" (if you say "I lived a rich life" you are strongly implying that this was at some point in the past and does not continue till the present)
- "I have read that book"
- "I have never eaten an egg"