In the recent years, researchers proposed a number of successful methods to perform out-of-distribution (OOD) detection in deep neural networks (DNNs). So far the scope of the highly accurate methods has been limited to classification tasks. Attempts for generally applicable methods beyond classification did not attain similar performance. In this paper, we propose a task-agnostic unsupervised OOD detection method using kernel density estimation (KDE) that addresses this limitation. We estimate the probability density functions (pdfs) of intermediate features of an already trained network, by performing KDE on the training dataset. As direct application of KDE to feature maps is hindered by their high dimensionality, we use a set of channel-wise marginalized KDE models instead of a single high-dimensional one. At test time, we evaluate the pdfs on a test sample and combine the resulting channel-wise scores with a logistic regression into a final confidence score that indicates the sample is OOD. Crucially, the proposed method is task agnostic as we only use intermediate features without requiring information on class labels nor the structure of the output, and attains high accuracy thanks to the flexibility of KDE. We performed experiments on DNNs trained for segmentation, detection and classification tasks, using benchmark datasets for OOD detection. The proposed method substantially outperformed existing works for non-classification networks while achieving on-par accuracy with the state-of-the-art for classification networks. The results demonstrate that the proposed method attains high OOD detection accuracy across different tasks, offering a larger scope of applications than existing task-specific methods and improving state-of-the-art for task-agnostic methods. The code will be made available.