Although this is an active area of research, I wouldn't say new algorithms are invented every day, not good ones anyway. The invention of a new ML algorithm that is better than the rest in even some semi-important particular cases would be pretty big news.
Usually, known algorithms are adapted to a given problem. Adapting one properly can itself be an area of research (spam classification is done with classical ML algorithms, but it's not trivial to perfect, so is digit recognition etc.)
Regardless, it's hard to find a source that lists all the known, classical algorithms. There are a lot, and it's unlikely that an author somewhere lists them all. They usually list the ones they work with, or the ones they consider the most important.
That said, I'm going to try to give you a longer list, and I'm making this community wiki to encourage other people to add more.
- Naive Bayes classifier
- K nearest neighbors classifier
- Decision tree Algorithms(C4.5, Random Forest)
- Kernel Discriminant Analysis
- Support vector machines
- Logistic Regression
- Passive Aggressive Classifiers
- Gaussian Processes
- Neural networks
- The Winnow algorithm