Dino Park Tycoon is the single rarest US game release for the 3DO, but can readily be found for cheap on other platforms and there is little non-collector demand for it on the 3DO. Lucienne's Quest is the second rarest US release- more copies of it were made for the 3do than Dino Park Tycoon but unlike DPT the 3DO was the only platform Lucienne's Quest was released on. Combine that with the fact that it is a well regarded RPG, and one of the best games games for the 3DO according to those who have been fortunate enough to acquire a copy (which I can verify, it is indeed a great game!). Between RPG fans and 3DO collectors the demand for Lucienne's Quest is probably greater than any demand for DPT.
As for overall rarest 3DO games, that honor would almost certainly belong to the games released for the system in Korea only by LG late in the system's life. Info on some can be found here:
http://www.hardcoregaming101.net/korea/ ... any-lg.htm
http://www.gotwalls.com/korean_3do/
http://fz1-3do.blog.co.uk/2009/03/01/ar ... n-5673527/
I've seen copies of Lucienne's Quest on Ebay every now and then (an open but mint copy went for over $400 a few months back), and there was also recently someone selling a copy of Dino Park Tycoon for an outrageously high BIN of many hundreds of dollars. I have never seen ANY of the Korean only LG games on Ebay, though.
Going by the listings here:
http://www.rarityguide.com/3do_view.php
the games Lost Eden, Neurodancer: Journey Into the Neuronet!, Mind Teazzer, Olympic Soccer (a late release), and any of the 3 different Woody Woodpecker video-CD releases seem to be quite rare. Ditto for the games Mathemagic and Slope Stlye: An Interactive Learning Cube. And though it was said above, the adult games for the 3DO are also uneasy to find.
Running this page:
http://www.batracien.fr/collection/3do.php
through Google translate also yields good information about some of the more rare 3do games as well.
Something else to consider would be games and hardware for the ill-fated M2 system that was to be the successor to the 3DO, as actual M2 units do tend to show up for sale online every now and then- Gamesnipe.com has had more than a few listings for them, and one can be seen right now for sale here:
http://www.ebay.com/itm/Panasonic-M2-3D ... 0747065610
M2 software also tends to show up every now and then as well, though it should be recognized as being quite scarce in terms of availability.
Hope this all helps!
EDIT:
I found a screenshot of my My Ebay Watchlist from several months back (Tip: always take screenshots of your watchlist before clearing it

) and it includes the ending acutions of several 3DO games I was watching from a seller named zhadnost, who was selling his entire collection of 3DO games. I remember that all the games were in pristine condition complete with longboxes and all but had been opened and played. The number of bids and auction end prices I have are:
CIB Virtuoso: 14 bids, $66.00
CIB Robinson's Requiem (an RPG): 21 bids, $102.50
CIB Lucienne's Quest: 26 bids, $377.00
CIB Strahl: 10 bids, $86.00
CIB Wing Commander III: 18 bids, $34.00
CIB Phoenix 3: 26 bids, $80.00
The seller had a ton of other games, maybe contacting him (or her?) would yield more information.
Also, the CIB copy of Dino Park Tycoon I mentioned above was listed with a BIN of $479.99 and did not sell at that price- which might provide an upper limit for a price on that particular title.