I'm a 1099 'contractor'. Some of my 2018 travel expenses were paid by me in 2017. Do I deduct those expenses in 2017 even though I have not taken the business trip yet?

[Anita01]

As a cash basis taxpayer, you deduct expenses when paid, so you would take this expense in 2017.  If it turns out that you don't take the trip, you can always reverse the expense next year as a negative entry under travel or miscellaneous in 2018.