Cancer classification is important in biomedical research because it can support diagnosis, disease stage classification, and treatment planning. A classification method is even more valuable for practical purposes if it is based on noninvasively or less invasively obtained features instead of invasive biopsies. In this study, machine learning algorithms were applied to two biomedical datasets for cancer classification and to examine how the structure of the data affects classifier performance. The first dataset is the Breast Tissue dataset, which represents a low-dimensional classification problem with 106 observations and 9 predictors. The second dataset is an osteosarcoma DNA methylation dataset, which represents a high-dimensional classification problem with about 480,000 CpG features and 15 samples. Logistic Regression, Support Vector Machine, Random Forest, and K-Nearest Neighbors were applied and compared using accuracy, precision, recall, and F1-score. Principal Component Analysis was used to reduce the dimension of the DNA methylation dataset before classification. The results showed that the machine learning methods performed more reliably in the Breast Tissue dataset. Random Forest and Support Vector Machine had the highest accuracy of 0.7895, while K-Nearest Neighbors had the lowest performance. For the DNA methylation dataset, the model performance was not stable across the different train-test splits. Even after Principal Component Analysis, the results changed depending on how the data were divided and how many principal components were used. This shows that high-dimensional biomedical data with small sample sizes can lead to unstable model performance. Overall, this study shows that machine learning is effective in cancer classification, but the results obtained must be interpreted and adopted carefully, keeping in mind the limitations of such algorithms under certain circumstances, especially when the number of features is much larger than the number of samples.