Music
For music, all I know about as services are iTunes (which I've never used), I've bought a few Japanese MP3 tracks on Amazon UK, but the selection is very limited, same goes for music.google.com. But if you find what you're looking for, go for it!Of course, there are other things to consider - sometimes CDs come with a DVD, or there's a first press edition that comes with extra bonus items (e.g. a poster, bonus tracks), so don't forget to look out for those.
Console Gaming
Nintendo: Wii U, 3DS and a DSi-enhanced DS games are all region restricted. DS wasn't, GBA wasn't. I don't have any modern import Japanese Nintendo consoles, so I don't know whether if you try to connect to the eshop with a Japanese Wii U or 3DS from outside Japan, you get to the Japanese eshop.
Microsoft: About half of all Xbox 360 games are not region restricted, and many people are unaware of this. The shop Play-Asia handily note on the page for each game they sell which games work in which region. You don't have to buy there, use their site for research. Notably, most arcade shmups by Cave are region free specifically because they know they have a worldwide cult following, but not necessarily one big enough to localise for each region. You can create different region accounts for Xbox 360 for the different content, with an American 360 account, we managed to download and play Aegis Wing, which is not available in the European store.
The original Xbox was region restricted. The Xbox One won't be, but don't expect to be importing Japanese Xbox One games.
Sony: This company used to be awful. The PS1 and PS2 were region restricted, then the PSP and PS3 weren't but instead they forced retailers to stop selling goods from Asia to the EU because they wanted to keep prices high. Nowadays, they like having customers. The nuances are going to take a while to explain, so that's why I left this for last.
The PS3, PSP and Vita are all region-free, there is one game I know to be an exception, which is Persona 4 Arena. You can set up one Playstation Network (PSN) account per region - please google how to do this because it's changed since I did it. With different region accounts, you can use the Playstation Store for the corresponding region, and get access to buy games you wouldn't ordinarily see. The PS3 will let you gather together and play all the games you have installed for all regions without any hassle.
The PSP and Vita however... If you are playing games from physical media, they work immediately. For digital games, because each handheld can only be attached to one account at a time, things are more complicated. Unless you own several PSPs/Vitas and dedicate one handheld to each account, you're going to have to do some account switching and memory-stick-switching to go from one game to another.
Another thing to look out for - the PS3 will play PS1 games, but the region restriction of the PS1 applies to physical discs - but oddly enough, not to downloadable games. So for example you can play Japanese PS3 games on a European PS3, that's simple enough. If you have a physical copy of [Tokimeki Memorial] for Japanese PS1 and put it into your European PS3, it won't work. But if you create a Japanese account on your European PS3, and use the Playstation Store with your Japanese account to buy a digital copy of [Tokimeki Memorial] for PS1, you can play that on the European PS3.
Lastly, your DLC must match the version of the game you bought. For example, if you buy an American copy of a game which is also available in Europe (e.g. Disgaea 3), and you want to buy DLC, you must log into an American account and buy the DLC. European DLC will not work on an American copy of the game on a European console.
Weird restrictions, huh?
To top this off, as far as I am aware, if you want to pay by credit card on a PSN account, it has to match the region. I don't care about this, because I don't like to give video games companies my credit card details anyway. The day after the Playstation Network accounts first got hacked, I received a phone call at work from my credit card company asking whether I'd just spent some money in a supermarket in Japan, and we cancelled the card.
I buy PSN wallet top up cards to fund my PSN accounts. I buy US and Japanese ones from Play-Asia because they have the best prices and the redeem codes are instant. I buy UK ones from GAME because I'm collecting loyalty points which eventually add up to free stuff.
The same goes for Nintendo eshop cards - I buy my UK ones from GAME for eventual money off.
For Microsoft points, I'd usually buy UK redemption codes from Amazon or Play.com because you'd get a much better deal there than just buying from Microsoft directly. e.g. 2100 points would cost £16.87 on Amazon whereas it would be £17.99 from Microsoft in the Xbox 360 interface. Now that Microsoft have stopped using points and gone to paying with money... pre-existing points cards are said to still work, but I haven't bought any.
Computer Gaming
Steam is the big platform if you are a PC gamer in "the West". If all you want to do is play ports of console games which are already released in English, install Steam, browse and search for the games you want, add them to your wishlist, and wait for Steam to have a big sale so you can scoop them all up for very little money. They usually have a big sale in mid-summer, a big sale in mid-winter, and smaller sales in between. As well as ports of console games, there are also some Ys games, some doujin shmups, and Recettear - the item-shop haggling / debt-repaying / dungeon crawling game which I've played over and over and would like to once again recommend to everyone.Steam is nothing in Japan. There's no Japanese interface, they don't sell the big name games in Japanese, as far as I'm aware there are no games on Steam that cross the boundary into pornography, etc etc.
When you say Japanese PC games, I think visual novels, those kind of adventure games. I also think "things they don't allow on consoles (especially since Sega stopped making them)", "touhou", and "small team experimental indie projects".
When it comes to visual novels - there are the official licensed English versions of games, there are the fan-translation patches that you can run against an original Japanese copy of the game to patch it into English, and there are the pre-patched English fan-translations, often of doujin projects where the original author has been asked and doesn't mind a translation.
Official licensed English VN sales:
Jast USA have been selling ero games since... well, since it became possible, back in the mid-1990s, and the focus of the games was pornography with a flimsy story on top. It's probably their fault that we started to call these things "hentai games" rather than "eroge". Nowadays, they also sell VNs that are mostly a good story (they have a lot of Nitroplus licenses), and sell digital copies - but it seems that their internal processes are stuck back in the 1990s, and turnaround between buying a digital copy from them and receiving a link to download from can take a week!
Manga Gamer sell VNs, have a strange way of categorising things whereby "Higurashi no naku koro ni ~ When They Cry" is designated "All Ages" because it doesn't contain sex scenes, though the torture, murder and so on would not make me want to categorise it in the same way. When they started up, I heard that their DRM was intrusive and the quality of their translations very variable, so I haven't bought anything from them.
Desura is a good site for buying downloads of indie games, it has a small selection of non-pornographic MangaGamer VNs and a larger selection of English-language-original VNs too. Eve Burst Error is there through MangaGamer, I'm glad that game is being "kept alive" this way.
DLSite contains tons of doujin material, including English versions of Hatoful Boyfriend (the pigeon dating sim) and other things. Prices are very good - cheap and swift. There's a lot of dodgy material on there, watch out and have fun.
For information about visual novel I might be interested in, I go to vndb.org, look at the tags to see if there's any material in the game which I'd find objectionable, look at the user ratings, and find out where it's available. If it's a game that needs fan patches, it'll be listed under tlwiki.org and there may be a page dedicated to it. Additional information if there are problems is sometimes available at fuwanovel.org.