The sound you are hearing is a standard IDE/E-IDE HDD "thinking" sound, which is perfectly normal. As for the constant, repeated clicking in your first video that does not stop, that is a bit unusual if you are not running anything. I would keep an eye on it. Some programs like Minecraft have a weird habit of doing that while being open, but if no programs are being used, this is not normal activity.
As for being worried, I wouldn't be yet. If you start experiencing weird behavior or different noises, then it may be time to get a new hard drive after backing this one up. In the mean time, just monitor it and see how often it makes that sound in a repeating fashion like that, rather than in the normal, sporadic and random intervals. Also check and see if you can track down a program on your computer that is causing it when it runs. If all else fails and you feel overly-paranoid of a system failure, do regular backups. You don't necessarily need to replace the hard drive right away if you have everything backed up on a regular basis.