That's kind of a difficult question to answer, but I'll give it a shot.
I like their slowness, they don't respond quickly like so many other plants where you can see big changes in a few days or a week or so. You always keep wondering if you "got it right". When they do respond, it's just the best feeling.
I like the research whenever I get a new plant or think about some new plant. I always end up learning so much more than just orchid culture or orchid stuff.
I like the people. Most are quite odd in a very good sort of way. Most are very intelligent and have a great sense of humor. Some are just WAY ODD, but still in a good sort of way.
They help me focus and unwind. I'm kind of a wired person all the time. I really have trouble sitting still. When I do the daily check on the plants, I really feel myself slow down because I'm always looking for the smallest signs of someting happening. I really have to stop thinking about everythng else and just look.
Those are a few reasons.