A good place to start is Freem:
https://www.freem.ne.jp/They've been around for a long time and have plenty of stuff. The quality is specious but I've found a few gems there. My favorite is Vanguard Princess but that's not really a studying aide.
If you're interested in indie Japanese stuff you've probably already heard of 海底囚人, but in case you haven't, here's the link.
http://funamusea.com/I read a lot of these when I was starting out studying. I'm particularly fond of 大海原と大海原. It's a beautiful, emotional story.
A lot of Alice Soft's old games are freeware.
http://retropc.net/alice/The Rance series is particularly good, but everything here is worth at least checking out. Alice Soft is as classic as it gets.
The coolest, most obscure thing I know of in the Japanese scene are "Ghosts".
"Ghosts" aren't video games or visual novels, they're an entirely separate medium of expression.
It's a little hard to explain what they're like. The picture I posted is a ghost I use.
As you can see, they're kind of like a character that sits on your desktop and has conversations with you.
Ghosts range from cute and happy, to dark and melancholic, to philosophical and pensive. Some of them are quite lewd.
It's something you can't ever really experience unless you know Japanese, so if you're learning you should enjoy the privilege.
Here's the client:
http://ssp.shillest.net/Here's where you can download ghosts:
http://buynowforsale.shillest.net/ghosts/Everything I mentioned above is explicitly freeware.
There are also plenty of old great games and visual novels that are abandonware.
Pick up a good PC-98 client here:
http://emulation.gametechwiki.com/index.php/NEC_PC-9800_seriesI use Neko Project II.
Here are a ton of PC-98 games:
https://archive.org/search?query=pc-98&and[]=mediatype%3A%22software%22
If you don't know where to start, try YU-NO. Lovely game.
Let me know if you have any questions and I'll try to answer them.
Good luck with your studies!
