Eliminating the shower door and curtain from a shower enclosure has a lot of benefits. There's less for you to clean, you get more light in the shower stall, you don't have the curtain slapping against you if it isn't weighted, and there's a much smaller chance of mildew forming or scale building up in places that are hard to clean off. But no door and no curtain both mean that you need to do something to prevent water from spilling and splashing over everything. You've got three options.
A Partial Shower Wall
One option is to install a permanent partial wall that blocks the spray from the shower. So, the stall would have an open door, but there would be walls on either side that prevented spray from coming out. The walls can be glass, glass block, or tile. Sometimes the side of the stall has a permanent wall and the side opposite the showerhead is open; other times, the opposite side has a full wall while the side of the stall has a partial wall. It really depends on your bathroom layout and the size of the stall.
Overlapping Glass Block Walls
If you've got the room, you might be interested in having a stall with overlapping glass block walls. Imagine the side wall of the shower stall curving around at the back to partially block the end of the stall, and you have to walk around that wall to get to the entrance. This does a marvelous job of keeping water in the stall, and it's a nifty way to decorate the stall as well. Plain glass blocks alone look nice, but you can add many different colors and form patterns in the walls as well.
A Wet Room Instead of a Bathroom
If you have a very small space and want to get rid of doors/curtains because they take up space, you can try transforming your bathroom into a wet room. This is a common configuration in Europe in which the shower, toilet, and sink are all in one smaller space. You have the sink and toilet as usual, and then the shower head is in a space to the side of the toilet, with a floor drain in the middle of it all. These work well for very small spaces where you can tile all of the bathroom walls. Make sure the showerhead is as far away from the main door as possible.
Contact a shower enclosure company, such as Hurricane Glass and Showers, and discuss your options. They can install the type you prefer or remove your enclosure if you're going to have a wet room. The result will be a shower that is easy to use and clean.