To date I've encountered about 5 different types of OBI.

1) The triangle OBI
2) Ring OBI (glued on the back)
3) Left side folded OBI
4) Sticker OBI
5) Top folded OBI (identical to a left side OBI but placed on the top edge of the cover with writing in that direction)

Personally I like the ease with which the triangle OBI can be removed if you so desire and also the fact it cannot easily be copied.
The folded OBIs are so easy to copy that quite a few LDs sold on Ebay are not actually originals....particularly used Japanese LDs being sold from the US.
You can usually tell from the quality of the ink, thickness of the paper, overall size or how it has been trimmed along the edges if it is an original OBI or not.
The ring OBI I hate because it is quite difficult to put back on a LD without damaging it unless you take it apart by breaking the glue joint on the back.
The sticker OBI is also not a big favourite of mine as they seem more of an afterthought and are often missing if the shrinkwrap or outer wrap is not intact.

Of the 5000+ LDs I own, about 3200+ are Japanese releases so I have a large pool of discs with OBIs to compare.
Now some of those Japanese releases never came with any OBI from new however that only represents a tiny portion.

The vast majority did come with an OBI and from inspecting the discs I have come up with the following approximate timeline for the various OBIs:

Triangle OBI 1980 - 1984 - have a few much later such as Whitesnake trilogy 1st & 2nd editions from 1989 onwards
Ring OBI 1983 - 1993 - have a few much later such as 1999 'Mariah Carey - The Ones' or 1999 'Yes - Union Tour'
Left Side OBI 1984 - 2001 - definitely the most popular and the longest in use OBI
Sticker OBI 1988 - 1999 - very popular by certain publishers such as Videoarts
Top Folded OBI 1995 - 1999 - far less common than the left side OBI and only used in later releases

Would be interested if there were any other types of OBIs and if anyone agrees/disagrees with those approximate timelines.

When you are concentrating on a single genre of disc, you may fall into errors through statistical bias, due to the practices (for example) of particular publishers. From my library, which is biased towards anime, I observe that the "Future Boy Conan" LD release circa 1990 (example) have the triangular corner-obi, and that some Bandai series releases (such as Gundam 0083) switch back & forth between top-folded & side-folded.

Um...you know those things are meant to be thrown in the trash immediately, right? I can't believe people would actually bootleg an obi. That's...crazy. Did they bootleg the store receipt too?

Anyway, to the original point, I don't really think its so much an age thing. As publius pointed out, certain publishers have certain preferences. Example: my copy of Macross Flashback 2012 (mid-90s reprint) used the triangle obi just like the original pressing (1987). Also, you didn't mention the right side obi, which Emotion did on several occasions.

I think a more accurate measure of an LD's age are the same factors for non-JP releases; Look at the catalog number. Does it have chapter stops? Does it have digital sound? AC-3? DTS? Is it widescreen? That sort of stuff. Using these factors you can %90 of the time guess the age of the LD by an accuracy of two years or so.

BTW, vinyl records all had obi usually too (12"s anyway) nearly all of which are left sided.

Also, does it have minutes only or minutes seconds.

I'd agree with the all of the comments made.
The more I looked at my own collection (which is mostly music LDs) I found inconsistencies in when certain OBI's were being used.
It did seem to be biased towards specific publishers. In particular Sony completely ignored any rules other publishers adhered to and did their own thing.
They were still using ring OBI's right up until the end when every other publisher (it seems) had moved on.
Also for years Sony refused to refer to this format as Laserdisc but instead called it Videodisc.

Overall I'd say if you are using OBI's to gauge the approximate age of a laserdisc, you need to tread with caution.
Whilst there is a general trend of moving from triangle OBI -> ring or left side OBI -> sticker OBI -> top side OBI it didn't always work out that way.

For what it's worth, the oldest Japanese disc in my library with an obi is a 1985 King Records release with the "ring" type. Given that obi means belt, & that this is the type which seems to be typical of LP packaging, I'd expect those to be the oldest.