Me, no. Luggage stolen in Brazil, local police report apparently wasn't sufficient. Also Brazil, hotel charged me for extra nights after I'd returned to UK, insurance said they couldn't verify my claim and I should've reported it to the police in Manaus (from home??) Jewellery stolen on plane home from Thailand, insurance said it wasn't covered as I'd left Thailand and only reported to the police at home.
Easyjet flight delayed by 8 hours, neither the airline nor insurance would compensate. I tried fighting that one but they wore me out.
Caught amoebic dysentery in Thailand but the wonderful doctor was so cheap, it wasn't worth claiming.
I was mugged at the same hotel in Manaus. The only worthwhile thing he got was my credit card, and Visa were fantastic - froze the missing one, gave me an emergency code for an ATM, and couriered a new card to me (which was then skimmed by the hotel management!)
The other replies here are VERY strong illustrations of why we need insurance, though, and I'd never travel without it.