I frequently wash and block something I am knitting while it is still on the needles. I do this when I am concerned about how my project is coming out. Something doesn't look right, and I don't want to go farther until I am reassured that all is OK.
My Catkin Shawl was a good example. The 'corners' of this shawl use lots of slip stitches to create the graphic stripes. The 3 corners looked a bit weird on the needles, but once I started binding off, I realized that they were curling and twisting oddly. The image below shows the shawl unblocked, still on the needles (see them on the right?).
Here is a closeup. At this point, there were 545 stitches on my needles, and binding off was taking forever. If I had to redo that bottom section, the two-colored part at the bottom (the trickiest part of the pattern), I wanted to know before I finished binding off.
So I decided to wash and block part of the shawl while it was still on the needles. Here is how I do it: I put the part of the shawl I wanted to block in a basin of water, taking care to keep the needles out of the water. In other projects, I have put the cable part of a circular needle in the water, but I keep the needle tips, especially wooden ones out. I position the knitting bag in such a way that it helps hold the needle tips out of the water. I have used a ziplock bag on the needle tips for added protection, but didn't need to this time. You can see the needles on the right in the image below.
I used cold water with no detergent (I don't want to rinse) and left it to soak for ~15 minutes. I then removed the shawl, gently squeezed out the excess water and then rolled the wet part in a towel.
Then I laid the shawl out to dry on my guest bed. I did not pin it, because I didn't plan to pin this shawl when it was complete. If it had been a lace shawl, I would have pinned the wet part. At this point I was encouraged because when wet, the curly corner had relaxed and lay flat. But what would happen when it dried?
Fortunately, it is very dry where I live, and shawls dry quickly. I was VERY pleased to see a nice flat corner on my dry shawl, below. Note: it is important to make sure your piece dries completely. Wet and damp wool behave differently than dry wool.
And the corner remained flat when I held it up so it hung loose. I was amazed because I was pretty certain that I would have to redo that bottom section, hours and hours worth of knitting. I was so glad that I took the time to go through the blocking-on-the-needles step because it ended up saving my lots of time and aggravation in the end.
The first time that I tried this was with a bottom-up seamless vest with a complex cable pattern. On the needles the cables looked messy, and I was unhappy with them. I was about 6 inches up the vest and was ready to rip it out, when I decided to try blocking it on the needles. The washed and blocked cables looked terrific, and I completed the vest. As I was knitting, I enjoyed looking back at the washed and blocked 6".