Modern DSLRs are made with autofocus in mind, as a result viewfinders are not quite as bright (since light is sent partly down to the AF sensors) and don't have the built in manual focusing aids to help lock on the focus. As a result manual focusing today is a bit harder than it was in the past.
Most people using modern DSLRs are going to be using auto-focus for the majority of their shooting (there will be exceptions of course) and I would put serious time into learning how best to control your cameras AF system to its best effect. In the end in the right conditions and when used well the AF will be faster than you are and likely more accurate too.
Note also that an important part of this is going to be the specific camera body as well, lower end bodies with weaker AF systems and less AF points might well feel more limiting than those upper level bodies with more and better AF sensors to use.
Typical examples would really be anything - from sports and wildlife through to landscapes and portrait work; with some camera bodies even macro is becoming an option for auto focus.
However it will be fooled and there will be times its not practical/possible to use AF to proper effect, as a result this is when your manual focusing comes to the fore. Either as a small correction to an already auto-focused shot or as the main form of focusing.
Typical examples where manual comes to the fore would be - macro (typically almost all done manually), landscape, portrait
In the end you can see there is a lot of overlap and this reflects personal choices and tastes when shooting, as well as experiences.