As mentioned above, the "key money" is really getting to be a thing of the past.
It depends on the property. Personally I've never paid it and I would only do so for a place I truly loved, and even then only if I had no choice... I moved to a high rise last year and there was no key money, and no agency fee (or maybe 0.5?) Having said that, I searched for over 3 months and had a few "specs" that I wanted to be met: size, age, safety, floor, rent, distance to the station, must be Yamanote or inside, supermarkets, big windows, "gaijin" friendly... So yeah, I'm surprised it only took 3 months.
I tried to bargain (oh yes I did!) and they were really adamant about the rent being the publicized amount, not even 3% down, but they did offer 3 months half rent (50% off, and they'd give us 6 months half rent if we chose a 2LDK), which made no sense to me because it would "cost" them less to just lower the rent 3 or 4%. Anyway, many companies do offer "free rent" or "half rent" so always try to haggle! It's a myth that Japanese don't negotiate on prices/benefits. It's a bit like Yodobashi Camera, they won't lower the price, but they'll give you more points if you push them.
Either way, it did end up being a couple of months up front because of the deposit, the guarantor fee (as non Japanese without Japanese family we use companies to act as guarantors), the insurance and whatnots. I was happy to hear from another expat in the building that he renewed his 2 year contract without the renewal fee!!! Hope that sticks around for a while.
Regarding the deposit, my last place was a bit of a disappointment. I spent the whole weekend moving and then went back to clean EVERYTHING, leaving it spotlessly clean and the floor super shiny, no dust, no nothing... Only to find out that almost half of the deposit was always retained for cleaning and "buffing" the floor and such, there was NO damage whatsoever, not even a scratch. Should have saved the elbow grease.