The answer, as so many things and people are in the world, is simple. Get yourself some memorabilia!
The Japanese approach to TV and music is much for different to that of the Western world. Whereas in the UK and US you might have the bog standard toy from a particular show, or an iconic symbol that respresents the show (the Pokemon pokeball for example), Japan goes at least ten steps further.
There are toys. But there are also clothing items for men and women, calendars, sountracks to the anime (sung by the Japanese voice actors themselves, or seiyuu) jewellery, food and so on. In fact, pretty much anything that could be turned into merchandise pretty much is. And it's not just aimed at kids, which is the fundamental difference between the two shopping cultures.
My particulary favourite type of memorabilia is the Plushie. A plushie (or to give it it's proper name- Plush Toy) is basically as stuffed toy/cuddly version of a character. It doesn't matter who the characters are, more than likely there is a plushie version of them out there. Plus they come in all shapes and sizes, from tiny ones that could be attached to a keyring, to human sized plushies (a human sized Sasuke... *fans self)
Here are just some examples are bishounen plushies:
Ah... the Sasuke plushie- in fact, this is one of the more better ones out there... he just looks so cute. If I see this for sale at the London Expo, wild horses wouldn't keep me from buying him!
Abarai Renji from Bleach. I've already introduced you to one character from Bleach, now here's another. Renji is a vice captain, but it doesn't mean he should be taken lightly.
I like how they they've captured his moody face. He isn't always moody, he does it to look intimidating, but it's the look I like the most for it means time to fight!
The Inuyasha Plushie. Obviously not the best plushie in the world but you win some, you lose some. It does what its fundamentally supposed to do- look like Inuyasha, but there is one thing that sort of irritates me about it- you can't really see the ears. Maybe that's just the photo angle but Inuyasha without the ears is like Soaps without the rubbishness- it just doesn't work as well without it
Well, now you have seen some examples of memorabilia. If you have the hankering for some of your own, a site I would suggest to you is Tokyo Toys. They are based in Britain, import all their stuff from Japan and sell them for very good prices. They also do their own clothing range, so that's something to bear in mind. Happy shopping!