Enabled addons list for blender 2.79 in human-readable format:

enablist = [addon.module for addon in bpy.context.user_preferences.addons]
for addon in addon_utils.modules():
    if addon.__name__ in enablist:
        print ('{name} {ver} {mod}'.format(
            mod = addon.__name__,
            name = addon.bl_info['name'],
            ver = ''.join([str(v) + '.' for v in addon.bl_info['version']]).rstrip('.')))

Enabled addons list for blender 2.79 in human-readable format:

enablist = [addon.module for addon in bpy.context.user_preferences.addons]
for addon in addon_utils.modules():
    if addon.__name__ in enablist:
        print ('{name} {ver} {mod}'.format(
            mod = addon.__name__,
            name = addon.bl_info['name'],
            ver = ''.join([str(v) + '.' for v in addon.bl_info['version']]).rstrip('.')))

Update for 3.0+:

import addon_utils
enablist = [addon.module for addon in bpy.context.preferences.addons]
for addon in addon_utils.modules():
    if addon.__name__ in enablist:
        print ('{name} {ver} {mod}'.format(
            mod = addon.__name__,
            name = addon.bl_info['name'],
            ver = ''.join([str(v) + '.' for v in addon.bl_info['version']]).rstrip('.'))) if 'version' in addon.bl_info else None