Just my limited experiences:
I've built four major things from my own designs and two major things from plans.
The first thing I ever built was a shop table for my planer. I didn't have much else working, yet, so it's just screwed together and is rickety. I designed it myself, though. Wish I'd known about half-lap joints at the time. Maybe a plan would've helped.
The second thing I ever built was a table for my son, of my own design. I didn't get a plan because it seemed to be to be very straightforward. I looked at a number of other children's tables to get the basic dimensions, and designed a big, heavy library table with mortise and tenon jointery - but sized for a two year old. I'm very proud of it.
The third thing I ever built was my son's bed. I looked for plans as a basis because there was a lot about making a bed I didn't want to learn by messing up $250 in cherry. I had no idea how to distribute the loads, how big it should be relative to the mattress, or what knock-down jointery system to use. I got _The Bed Book_ and discovered that the first bed in it was exactly what the bed I wanted to build. I changed the design not one iota. I'm also very proud of that bed - while the design is not mine, I did select the wood, mill it and select and implement the finish. If I do say so myself, it's very pretty.
The fourth thing I ever built was some wall-mounted cabinets for my shop. I designed them myself. One of them is in the process of falling apart. I didn't do a dado for the backs, I just glued and nailed them on, and that wasn't sufficient for the stresses. I wish I'd spent more time looking at plans. Hopefully I'll be able to salvage the materials.
The fifth thing I ever built was an enourmous (6' x 2 1/2') planter for SWMBO. I designed it primarily to skimp on materials while allowing for a lot of wood movement while not actually doing any complicated jointery so that I could move on to a project I really wanted to do. Between you and me I realized after it was about 90% complete that, if you tried to pick it up in the most obvious way while it was full of dirt that it was going to fall apart, so I reinforced it with a bunch of metal L brackets. Yuck. I'm not very proud of it, although I am happy with how it looks. I looked at a lot of plans, and got a lot of ideas about how to design the drainage system for it, but I never really found plans that were exactly what I wanted, so I designed my own. I'm a big fan of the saying, "Experience is what you get when you don't get what you want." This project was good experience.
Finally, I'm building a bench along one wall loosely based upon Norm's "Miter Bench and Storage." It's not exactly the same, but it was very convenient, for such a large project, to have someone else provide a materials and cut list. I'm also paying a lot more attention to how to do things like build drawers so I don't make similar errors to what happened with the cabinets.
To me, there's two basic reasons to use plans. First of all, I know WAY more about woodworking than any other person I know. Unfortunately, that's not saying much. Rather than teaching myself how to design at the same time I teach myself craftmanship, building from someone else's plans allows me to focus a lot of time on the craft of building and not sweat about design details.
The second reason is that the plan is available and is exactly what I need. Most of my woodworking at this time has a utilitarian base - I'm building furniture and fixtures I need. If I see plans that are for almost exactly what I want, it's a definite time-saver to use them as a starting point. Since I'm researching plans anyway to get an idea of what the design elements are to consider, if I find exactly The Plan, why try to recreate it from scratch?
Do I hope to some day be able to just sit down and whip out a design for any project? Absolutely. But I guess in some ways this lets me apprentice myself to people like Jeff Miller or Norm Abram. The master designs, and I implement, and in implementing try to understand the design better.