Reading a thread on GoDiscussions about getting to SDK (Single Digit Kyu) I saw a bunch of good recommendations, mostly around a few books and doing problems.
I realized that I hadn't done any tsumego for quite a while, so I headed over to GoProblems to try a few. I set up a set of 50 problems from 30 kyu to 15 kyu and got 49 right. Next I tried 20 from 12 kyu to 10 kyu and got 6 or so.
Wow! Tsumego really does have difficulty levels! I don't think I really believed that before. I was successful at tsumego that focused on killing "dead shapes" and finding cutting points but generally failed on liberty races. This is a huge, clear indication of a path to improvement.
Seeing that there were situations on the board I wasn't comfortable with helped me see others. In the past I think that when there was something tough to read, my brain just sort of glazed over a little and I convinced myself it wasn't important. Now I am trying to alert myself when I get into a position that is over my head.
I noticed that I can't clearly tell when an unfinished corner is alive. I am not confident that I can succeed at a 3-3 invasion. I also need work on liberty races.
So, although you hear it from everyone, doing tsumego can help your game. Tsumego actually does have strong correlation with skill level. So, if you work on problems that are a bit harder than you can do, and you learn how to recognize and solve those situations, you will have improved!
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