The Fantasy Flight Games license to Anima: Beyond Fantasy expired in 2016, and currently the game is out of print in English. The makers have been looking for a new publisher/translator, but in the meantime, keep passing around the books.
The Fantasy Trip went out of print in the 80's but survives to this day, thanks largely to PDFs of the rulebooks circulated between friends and via the Internet.
This was often out of necessity. For example, the original 3rd Edition Ork codex was released in mid-1999. It remained the "current" codex until a 4th Edition was released in late 2008.
Warhammer Quest likewise.
All of Games Workshop's Specialist Games (including Battlefleet Gothic, Gorkamorka, and Epic 40,000 among others) and all models associated with them were discontinued in 2013 (purportedly because GW was switching from pewter to resin for their models and didn't want to recast all the models for their old games). Blood Bowl was eventually re-released, but a rumoured revival of Battlefleet Gothic failed to materialize and most of the less popular Specialist Games are presumed to be gone for good. Some enjoy strong cult followings and secondhand models can fetch prices online well above and beyond their original sticker-price (which is particularly impressive given Games Workshop's usual pricing schemes).
Games Workshop also has a tendency for incredibly small production runs for tie-ins and printed materials, and only the novels and rulebooks ever get digital releases. A product selling out in minutes and never being released again (or in rare cases getting a similarly tiny reprint) happens all the time, leading to ludicrously high secondary market prices (many times the sticker price) and widespread use of scans.
Dungeons & Dragons 3.5 edition and all prior editions are completely out of print. With 3.5's staggering popularity, prices for used copies of the more common books are slowly on the rise. Wizards of the Coast used to sell PDFs of all of its current products and any TSR products as well, but they were all pulled from websites like RPGNow and DriveThruRPG in Spring 2009.
Every edition has this. Check the prices on eBay for some of the favored old AD&D modules and editions. Check the prices for Planes of Conflict or Menzoberranzan or The Ruins of Myth Drannor or Spelljammer: Adventures in Space. As of 19 Sep 2011, the asking price for some of these sets (the original Ravenloft boxed set or Hellbound: the Blood War) is higher than the retail price for the products when they were new.
In January 2013, WotC opened a DriveThruRPG subsite, "Dungeons & Dragons Classics", and started releasing supplements from every D&D edition, up to and including 4th, with the intent of having hundreds of titles available.
Star Wars d20 RPG articles and modules posted on the internet by publisher Wizards of the Coast were taken offline by the company when the license expired in May of 2010. They're still out there, kept online by fans who saved them before they were taken down.
The BattleTech magazine Battletechnology falls into this category as well. Originally published in-house by FASA, it was later "farmed out" and passed through several different publishers before finally ceasing publication, leaving behind a tangled mess of ownership. The result is that it will never be compiled or re-printed. Furthermore, by Word of God, material from Battletechnology will not be used in the Tabletop Game unless it is non-contradictory and the original creator can be tracked down. (Several mechs from the magazine have appeared; in those cases, they were either created in-house to begin with or the writer is now a member of the BattleTech creative staff.)
The original Dune board game is considered a classic, but is direly out of print, and going to stay there due to rights issues.
Two of the first movie cards, namely the "Pyramid of Light" and "Blue-Eyes Shining Dragon", haven't seen a booster pack/Promotional release, and the only ones existing are the ones who went into the movie, and kept them in good condition, or mostly worn out.
Quite a number of cards are only released as short print in some areas. Usually these are magazine promos for the likes of Shonen Jump, which just went all digital and means its last few promos got even less time to saturate. If you're in the US, good luck getting Slifer, Obelisk, or Ra without forking out some serious cash.
Far Future Enterprises is doing a good job keeping much of Traveller available in .pdf format, but the licensed work of Digest Group publications during the MegaTraveller era is unlikely to ever be included. A fan bought the rights when DGP folded and has refused to sell them, to the point that Marc Miller has declared DGP materials uncanon, only usable in Broad Strokes fashion.