Some of the most popular classifiers in machine learning, in roughly descending order of usage, are:

1. Logistic regression: Pros - Simple to train and interpret. Cons - Makes strong linear assumptions so may not fit complex data well.
2. Decision trees: Pros - Easy to interpret, can handle nonlinear data. Cons - Can overfit the data easily, may require pruning.
3. Naive Bayes: Pros - Very fast to train and predict. Cons - Makes strong independence assumptions that are often violated in reality.
4. Support vector machines: Pros - Often leads to good performance, can handle nonlinear data. Cons - Can be complex to tune and interpret.
5. Neural networks: Pros - Can achieve state-of-the-art results, especially with deep architectures. Cons - Typically black box models that are hard to interpret. Prone to overfitting without careful training.

The pros and cons listed here are generalizations - the performance and suitability of a classifier will depend a lot on the specific problem and data in practice. But this covers some of the most popular classifiers and their major advantages and disadvantages.
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