Download LOL Recorder from this site http://www.leaguereplays.com/ as mentioned in previous answers. For the best results though you should go into the options (the cog wheel in the corner of the main page on LOL Recorder) and turn on:
- Record While Spectating
- Record All Matches in Specmode
What this will do is allow you to record while just purely spectating as you asked, but will also give you the recording in the mode in which you spectate (i.e. Specmode), if the Record in Specmode box is not checked, you will only see health bars of friendly and enemy champions within a certain proximity of yourself, before they disappear, you can't see the total gold of both teams, and the UI just doesn't look as nice.
If you are unaware of what specmode is I will elaborate. Specmode includes:
- A very nice UI that allows you to see BOTH teams all the time (not just your own)
- Allows easy view of how long wards will last
- The UI also has a nice centerpiece that allows you to see the gold currently owned by each champion (even enemies) and how much they have acquired throughout the entire game, as well as all items owned by all champions.
- Rewind and fast forward mode
- A camera that if left untouched will follow the action and jump around the map to different champions without you touching a button (called directed camera)
- Total gold obtained by each time for easy telling which team has the gold lead
- An easy counter for how many towers each team has taken down
- Colorblind mode for anyone that is colorblind, allowing the purple team to become the red team
- More I'm sure that I just can't think of
Record in specmode will also allow all the games you play yourself to be recorded in this fashion, for very improved reviewing of your own games. I hope I've provided sufficient information on this subject and that you enjoy LOL Recorder and Specmode recordings.