First let me give the definition of Data Science -
“SQL is all about data. Statistics is all about inference. Data Visualisation is all about insight. Machine Learning is all about prediction. Communication is all about decision making. Data Science is all the above.”
So, you see it has no algorithm of itself. But there is a machine learning part where some algorithms are used. I think your question was about the machine learning algorithms.
There are some important, classic algorithms such as - linear regression, logistic regression, decision tree, K-Nearest neighbour, neural network, naive bayes, support vector machine[these all are for supervised learning] .