Keep in mind comments are not posted on all youtube videos. Comments can be disallowed by they youtube user posting the video on youtube. But, if comments are not allowed, this fact will be displayed below the video. Anyway, just thought I'd mention this in case this might apply to videos where you saw no comments and overlooked the notice that comments were not allowed.
Regarding the comments about needing a Google account, that only applies to people who want to upload video content to youtube or post comments on youtube. I don't believe you need to be signed on to a Google account to view comments posted for a video.