I noticed a few things.
1) My digestion improved after about a week. But during that week, I became really frustrated that my typical 'elimination' time completely changed i.e. I was used to going to the bathroom in the morning, after coffee, but now found myself having to go in the evenings.
2) My productivity took a massive nose-dive until I got used to not drinking coffee, and then, despite all of the blogs I read on the subject, it did NOT return to "coffee-baseline". I no longer felt like there was a funk, but I also was clearly not performing at the same level as while I was drinking coffee.
3) I noticed I started getting depression like symptoms after I had completely weaned off of it. I don't think this would happen to everyone, but I think one of the primary reasons I was drawn to coffee in the first place was that it seems to have an anti-depressant effect on me when I drink enough of it (really any caffeine/stimulant does this though)
4) I primarily drink coffee during the first 8 hours of my day, so after a month of cold-turkey, I found that I had an intense time trying to stay awake around lunch time, with a second-wind of energy returning to me around 2PM. I found that I felt more energetic in the last 4 hours of my day prior to bedtime. Because of this, I found it more difficult to get to sleep, because I had grown accustomed to that exhausted feeling I would get near the tail end of the day, so adhering to a set bedtime was a challenge.
5) Probably the biggest gain was a massive boost in right-brained thinking. What I mean by that is, while drinking coffee, very clearly defined, left-brained tasks (like researching a problem, coding, writing something down, exercise, etc) were what I preferred to do. But after eliminating coffee for a while, I found that I was thinking a lot more creatively about things, and daydreaming more. Coming up with unique ideas for things I'd like to do/make. The problem with this was that I no longer felt the drive/motivation, or the mental acuity to actually do them. I felt like I could have better conversations with people, and was friendlier overall. I just basically wanted to draw pictures and hang out with my friends all the time. I enjoyed lunch more and noticed the subtleties in food a lot more.
There were a lot more very small effects. Ultimately I returned to coffee/caffeine. If I could work in an industry where I could maintain the same standard of living but could rely on purely physical strength and skill, rather than mental information work, I'd probably eliminate stimulants altogether, and be healthier for it. I just find that to be competitive and basically maintain my job, I need the stimulants as a crutch, because there are so many more people who are better at development and naturally interested/motivated in it more than me.