There is no doubt that we store a lot of sensitive data to our phones these days; from sensitive photos and personal emails to a social security number and banking statements. Therefore, there is definitely a lot of data in there that you would want to keep away from any prying eyes.
Encrypting your phone is the most reasonable and efficient option here. Even if someone steals your phone, encryption will keep your data absolutely impenetrable. Having to buy a new phone is a small price to pay compared to having your privacy intruded.