The only “format” that is capable of doing what you are proposing is DVDÂ±VR, and this is quite troublesome. DVD-Recorders (or drives, with software assitance) are able to record and play back this format, or a player that explicitly supports DVDÂ±VR discs, although compatibility with some standalones are not ensured. For more info, you could check out Wikipedia’s entry on DVDÂ±VR or search Videohelp for DVDÂ±VR.
For best results and compatibility, you are better off authoring a DVD-Video for each event that you are going to record. Although flexibility is lost you are guaranteed security in the fact that you will never overwrite a previous event and that DVDÂ±R discs are more stable over time than DVDÂ±RW.
FYI, a single-layer DVD (DVD5) can hold up to 2 hours of video in optimal encoding quality - which, in my opinion, is just enough for live events and such. Buying discs in bulk is pretty cheap nowadays, and getting a trusted brand as Wizzu has suggested will be well worth it.