Demand for goods on the Auction House may be down overall, but that's at least partly because the overall level of engagement among players is down. The biggest change, though, is a shift in what people spend gold on. While in the middle of an expansion people will focus on and strive for PvE progression or PvP goals, at the end of an expansion, players tend to try out new parts of the game. Raiders will play RBGs, players will collect achievements, pets, and transmog gear, and everyone starts alts.
PvP: The most obvious way to make money off players shifting into PvP is to sell crafted gear. Leatherworking, tailoring, and blacksmithing all have PvP blue gear that is typically used to fill in gaps while a new player works on their honor-bought gear. Every so often while idling around chatting with friends, I notice a stream of gold-letter "buyer found" notifications, indicating that someone just bought a whole set of crafted gear from me.
Another way to make money from new PvPers is to offer PvP gems and enchants. Most of the gear enhancements PvPers will buy are the same as PvE players; however, there are some differences. Yellow sockets not being ignored will be stat/resil, for example. Or maybe even straight resil. Some enchants might be resil instead of stats.
Alts: The most profitable things you can sell to alts are profession leveling tools -- raw materials, and if you're really ambitious, leveling kits. The easiest way into this market is to farm. Focus on late vanilla, Burning Crusade, and Wrath of the Lich King zones. I paid a small fortune for Knothide Leather when I was leveling my leatherworker, and I just counted myself lucky that I only had to buy out the AH for a couple of days to get enough to get onto the next step.
The next way into this market is a little labor intensive but can be very profitable. Leveling kits can't be sold on the AH, but they sell like hotcakes to people who would prefer instant gratification to a lower price. It's a real skill to build them, but you'll find plenty of advice over at The Consortium, as well as a handy spreadsheet.
Lastly and possibly in conjunction with the first two options, you can try to be a market maker for profession leveling materials. You have two competing forces here: farmers who level through the places that generate the desired materials will want their money quickly, and people leveling crafting skills through these materials need a large quantity of mats all at once. Left to the open market, people leveling farming skills will have to relist their goods a few times to sell it, and people leveling crafting skills can't get enough materials in one crafting session to progress.
What you do to become a market maker is frequently buy materials as they're posted, and repost them in large quantities at higher prices, especially on the weekends. Because it's a higher price, it won't sell as quickly, which means you will at first buy more than you sell. Once you have built a nice stockpile, you can start reducing the price. This will increase your sales, and you can try to match them to your buying. This can be risky business and is definitely a long-term commitment. Random farmers will typically undercut your large quantities just enough to ensure they get bought, but you can get around this by not completely buying out everyone who undercuts you.
Transmog gear: Some items are incredibly popular among those who care what their character looks like. You can get Darkmoon replica gear, you can farm instances for BoE gear, or you can watch the AH for cheaply posted gear you know to be of value for its looks. Personally, I have less than no fashion sense; however, I am told that the list of transmog gear on Faid's blog looks pretty good and is in demand on many realms. There's a video there about how to import and use those lists, but it assumes you have (or can install) some addons.
The general way this market works is that you buy gear when it's put up for sale by someone who doesn't realize that it's actually worth to a much more affluent character, and sell it for what it's really worth on the AH. It can help to link it in trade chat once in a while.
Pets: There are a ton of pets that can be sold on the AH, and almost all the pets you know will be trainable and tradable in the next expansion. Players looking for pet achievements now tend to reliably buy the crafted and vendor ones that are sellable on the AH; list two on the first post of this thread is a good starting point. Also, you might be well served trying to get some BoP pets now so you can sell them on day one of Pandaria. You should be able to place just about any pet you know into a pet cage, allowing you to sell it on the AH.
Maximize your profits with advice from Gold Capped. Want to know the very best ways to earn 10,000 gold? Top gold making strategies for auctioneers? How about how to reach 1 million gold -- or how one player got there and then gave it all away? Fox and Basil are taking your questions at firstname.lastname@example.org and email@example.com.