Why do I love enemas (yes, I'm now to the point where I think I would start to miss them if I stopped)? There are many reasons.
The first and most obvious is that they are effective. Two enemas knock out most of what's in my bowels, and they do it quickly and usually pretty comfortably. Enemas take the bullet points on oral laxatives and kick it up a notch - effective (Oh, yeah), comfortable (usually, or at least not more uncomfortable than a stimulant), and you certainly don't have to wait overnight for the relief or wonder when exactly it will kick in. Now that I know my bowels much better I'm almost at 100% "quick and effective", because I can tell pretty accurately how powerful of an enema I'm going to need.
Second is that I really don't need to stock anything, at least for high-volume water-based enemas. Yes, for some of the high powered enemas I use when things don't work I do have to have supplies, but for most situations I have everything I need to get things started. Water and ideally a little soap, but in a pinch straight water works. This isn't as big of a deal now, but before I did have times when I wouldn't have any laxatives/suppositories and I would wait for too long before dealing with a bout of constipation. Going out to the drugstore when I'm feeling pretty miserable and looking it to buy laxatives never appealed, but with an enema I could take care of things anyway.
Beyond that comes the more private reasons, the ones that you're even less likely to talk about.
The enema is a highly ritualistic procedure, and for some reason that can be comforting. You can pop pills in an offhand way, but the enema is different. You get out the bag and connect the hose and nozzle, then get out the lube, soap and pitcher. You turn the water on to warm up, get out the towel and lay it out on the floor. Next the soap is measured out, and the pitcher is filled and mixed, with this repeated until you have your desired amount. Then the bag is hung, the tube "burped", and after choosing a position you emplace yourself on the towel. The lube tube snaps open, and some is rubbed on the nozzle and your anus, followed by a deep breath and the feel of the nozzle sliding home. A few more deep breaths, and the clamp is opened. Perhaps you'll move positions a couple of times, perhaps you'll have a mental dialogue with yourself over how full you're feeling and that you need to stop and use the toilet right now, but ideally you're a good boy or girl and work out a way to take enough of the enema to work - perhaps that new position, perhaps a break with deep breathing or panting, perhaps a gentle rub of your back, abdomen or butt. Perhaps even grabbing that very convenient penis (I usually just squeeze it like a stress ball, but sometimes masturbation can be effective). Then you wait. And wait. It seems like forever as your guts churn more and more. Then... blessed relief, until you're back for your second enema. Ritual. You know where it's going every step of the way. I guess suppositories have a bit of that - the getting them out, opening them up, assuming the position, and insertion - but it's nowhere near the same.
The enema is also a very good excuse to play with your butt. The focus is entirely on your anus and rectum from the start until the end. Based on your mood you can lube more or less, from a dollop rubbed quickly across the anal surface to a deep lube with two or more fingers. You can choose a nozzle that's thin, big and filling, slides several feet inside, or even inflates. You can have solutions that are hot, warm or cold, strong or weak, big or small.
As Viki V noted there is also the overwhelming mental presence of the enema.
I love the feeling of being in another world, like in a twilight zone when my mind and body are focused totally on feelings and sensations.
Once you start an enema the enema (and your guts and ass) is your world until it's over. If you have to you can use some of your mental energy to take care of other things, but most of your focus is what's going on in your butt. It's very hard to be stressed out when there's 2-3 quarts of hot, soapy water inside you and you're just riding the sensations and trying to keep everything from coming out too soon. I did see something else that hypothesized that the vagus nerve stimulation can also help some people, but I don't know how accurate that really is.
Then there's the feeling afterwards. I'm IBS-C, so this might not apply to others, but once the enema is over I feel right for a while. My gut feels more like it should, my appetite is back, and things are much more right with the world than before. This doesn't even touch on the other benefits, such as the fact that I now have a nice clean rectum that can be used for fun later, perhaps.