Various techniques to measure the force-extension relationship of individual polymer chains with the atomic force microscope (AFM) are compared. Reliable stretching force profiles can be obtained with the nano-handling technique, which involves imaging of the measured individual polymer molecules prior and after the force experiment. Results originating from the classical pulling technique, which relies on dense adsorbed polymer layers, must be interpreted with care. Comparison with the nano-handling technique reveals that the stretching response of individual molecules can be obtained with the pulling technique, provided the adsorbed polymer layer is dilute. For denser adsorbed layers, such experiments may not reflect the correct stretching response. The discrepancies seem to be related to polymer epolymer interactions and entanglements within the adsorbed layer. AFM imaging of the adsorbed layers can provide an indication concerning the relevance of such entanglement effects. Similar caveats apply to fishing experiments, where polymers are adsorbed to the AFM tip and not to the substrate.