Do transcription factors block transcription entirely?
Of course it's never 100%. The protein still has a measurable Kd for the DNA, meaning that there's always some part that's not bound (or some time that it's not bound. 

Besides that, you're talking about repressors. There are also activators, and they use many different mechanisms. The same regulator protein can even recognize different sequences of DNA and repress one gene more than another. Some can bind and actually recruit a RNA polymerase, some work only while they're binding small molecules. 

https://en.wikipedia.org/wiki/Transcription_factor or your molecular biology textbook might be a good place to learn more.