The LSE has some great short video tutorials on the following topics:
Introducing the SPSS User Interface
Creating New Variables and Entering Data
Recoding an Interval-Level/Scale Variable into a New Categorical Variable
Selecting Cases
Weighting a Dataset
Describing and Visualising a Single Continuous Variable
Describing and Visualising a Single Ordinal Categorical Variable
Comparing a Single Continuous Variable Between Two Groups
Correlation Coefficients
Generating and Editing a Simple Scatter Plot
Independent Samples t-Test for the Differenence Between Group Means
Simple Linear Regression
Multiple Linear Regression
Three-Way Cross-Tab and Chi-Square Statistic for Two Categorical Variables
Three-Way Cross-Tab and Chi-Square Statistic for Three Categorical Variables
Binary Logistic Regression