Not necessarily. In the UK (at least, at the banks where my fiancée and I hold accounts), you need to enter your PIN:
1) On the first transaction after activating a new card
2) On transactions above £30 (~$45) starting 1st Sep 2015 (however apparently some terminals have the former £20 limit hard coded and require a firmware update to increase the limit)
3) On random transactions
In the case of the random PIN verification for contactless payments, the frequency with which these are required isn't entirely clear. I have spent ~£100 over numerous successive contactless transactions (local store then rounds of drinks at the bar) without requiring PIN verification. In fact, I've never needed to enter my PIN - every contactless transaction has been automatically approved.
Over a typical week, I do contact a good mix of contactless and Chip-and-PIN transactions, so my risk profile might be different from someone who has, for example, a 80/20 contactless-to-chip ratio.
I'm unsure whether the PIN verification requirement is triggered by the application running on the card or by the transaction processor. This might actually be covered in the EMV spec [1].