Composting has reduced the sheer quantity of matter that goes into the trash can, of course, but the main reason I make very few trips to the dumpster nowadays is because there is no offensive, rotting trash that must be removed from my home.
In the past, if I threw a single banana peel in the trash can under my kitchen sink, I would have to take out the trash within a day or so - even if the can was barely full. Otherwise, the entire apartment would smell musty, and fruit flies and ants would appear. Now, with all my food scraps contained in the Bokashi bucket or the freezer, I haven't seen any pests for weeks.
As far as non-food trash goes, I save most sturdy plastic tubs for storing food scraps in the freezer, and save most glass containers as well. I empty a single paper grocery bag of recycling about once a week, which contains a mix of paper and various containers (the city does not require us to separate out different types of recyclables).
The remaining trash now contains little else besides dental floss and facial tissue*, and I can't even remember the last time I had to take a bag out to the dumpster!
* I have made several strides toward moving away from using disposables in my personal care routine. I have fairly bad allergies, and have tried using washable handkerchiefs instead of disposable facial tissue, but have not been able to fully convert away from disposables. Minimizing the use of facial tissue is something I'm still working on. And I'm not planning to do anything kooky regarding dental floss - yet!