SPM has a DICOM conversion utility that works with many different variations of the DICOM format (though probably not all... If you encounter problems, see below or try asking for help on the SPM Email List). If you access the conversion tool via the button "DICOM Import", you will be immediately prompted to select the DICOM files, with default options for the converted output. If you want more control (e.g. a choice of '.nii' or '.img/.hdr' output format) then access the tool via the batch system's menu:
SPM -> Util -> DICOM Import
If you have problems with SPM's DICOM Import, popular alternatives include:
At the bottom of the webpage for dcm2nii there is a longer list of alternative DICOM conversion tools.