The many different types of data visualizations can be roughly organized in several different ways, grouped here by their elements and the types of data they showcase. The below visualizations include some of the most common types but are no where near comprehensive.
More visualization types and their details can be found at:
Tables, sometimes known as data tables or text tables, are a simple type of visualization that allow for efficient display. Data is often first visualized in table format and then subsets of the dataset are visualized in more pattern-based types.
Tables
Source: Statistics Canada, Census of Population, 2016
Graphs use a reference system like x and y axes or coordinates and can show either qualitative or quantitative data. Common graphs include:
Bar graphs
Common graph type to show comparisons between categories.
Source: Statistics Canada, Census of Population, 2016.
Line graphs
Common graph type that shows trends, particularly over time.
Source: Statistics Canada, Labour Force Survey, 2020.
Scatterplots
Shows the relationship between two numeric variables like height and weight. Can also feature a trend line.
Source: Randomly generated data
Bubble graphs
Enhanced scatterplot, with another variable mapped to the size of the dot.
Source: World Bank, World Development Indicators, 2008.
Often used interchangeably with graphs (ex. "bar chart"), charts can show either quantitative or qualitative data without using a reference system like axes. Common charts include:
Pie chart
Commonly used to showcase the proportion of each category to the whole, where the percentage of each wedge should total to 100%,
Source: World Bank, World Development Indicators, 2008.
Word cloud
Shows the frequency of words in a text by having the size of each word proportional to the frequency of each word.
Source: Jane Austen, Pride and Prejudice, 1813
Maps display geospatial-related data, anything from a street-level to country-level and beyond, and can be enhanced using a variety of different types of maps. 
Source: Scholars GeoPortal
Dashboards are tools that combine multiple data visualizations to track, monitor, and analyze important data points and metrics. They often are set up to update automatically.
Source: Google Data Studio
Network layouts use a combination of nodes for data points and links between nodes to indicate relationships. Common types include:
Network graphs
Source: Gephi
Sankey Diagrams
Trees
Uses nodes and edges in a hierarchical format to showcase the system's relationship.
Tree maps
Uses spatial mapping to nest hierarchies and can showcase the proportion of a part to the whole.
Source: Randomly generated data
Infographics combine graphs and charts with visual imagery and text to quickly and clearly communicate information.
Source: Statistics Canada