I agree with other posters that carbs and sweets are physically addictive. So when you try to cut back a little bit, you crave them. The good news is that the less you have them, the less you crave them.
1) Make it convenient to eat healthy
I keep the fridge stocked with pre-cut fruit front and center. It costs slightly more this way but makes it way more likely that I will actually eat it (and reduces waste). You can also do this with prepared baby carrots or celery if that floats your boat.
2) Don't keep junk food in the house
I don't keep soda in the house. I tried variations like keeping soda in the pantry so it would be harder to drink, but it didn't really work. What works is just not keeping it.
3) Workout right before going grocery shopping
Whenever I workout I feel fit and more like eating healthy food. If I go grocery shopping when I feel like a bum, I am more likely to grab unhealthy snacks. When I just worked out, my body starts craving fruit and healthy things so that's what I'm more likely to buy. Actually in general the more I work out, the more weight I lose and not just from the workout - I eat healthier because I don't want to waste all my hard work.
4) Find healthier options that you enjoy
Instead of eating straight bran cereal that I don't like, I found a semi-healthy cereal with dates and raisins. Not as good as the bran but not as bad as lucky charms. I got this mint chocolate chip ice cream from whole foods made out of coconut milk - it is amazing and way healthier than regular ice cream. For soda, you can try going natural or switch to something like unsweetened tea (still flavorful).
5) Meet your nutritional needs at meals
If you aren't meeting your nutritional needs at meals you will feel hungry for snacks. Try eating way more veggies and adding lots of protein (lentils, beans, spinach, tofu - I'm a vegetarian). Then at least when you start craving you'll know that it's not necessary.
6) Distract yourself
Sometimes I eat out of boredom or habit. I haven't really mastered this one, but turns out even if you're eating pretty healthy foot a lot you still gain weight, or don't lose it. I try to engross myself in my work or something with varying degrees of success.
Good luck!