Because my income has taken a huge hit these last few months, I tend to only buy games on a good discount.
Game I have been looking forward to, and gets good reviews and good lets plays ~10-20% ($10 or less)
If I want the game but wont begin playing tonight 40%+ ($7 or less)
If it is one I like the look of 50%+ ($4 or less)
A game that sounds nice but no real urge 70%+ ($2 or less)
A game that might be good, but I would not normally play Free or bundled with a good few other games.

It is like Rouge Legacy the other day. I really want to play it, but at the price I just could not justify it to myself, as I wont probably have too much free time until Christmas because of work and University. A real shame, but the way life is right now.
I tend to buy more games in bundles because I get more for the price, even if most are games I have never heard of. I got Freedom Fall from Groupees a while back and I think it was my best purchase of the year.
The biggest problem is trying to buy DRM-free games at a reasonable price too.
Until the economy picks up (in reality, not just politicians heads) I have a very limited budget with which to buy things.

It's depend on the game quality and whatever I consider its original price to be a fair deal.

On an emotional level, if I see 50% or more I say "good discount" and if I see less than 50% I say "bad discount," but it always ultimately comes down to price. According to what I just said, today's indie gem promotion should seem like a bad deal to me, but actually, $12 is about the price I'm willing to pay to try that game, so I picked it up. If the undiscounted game was $60, with a 50% discount, I wouldn't have touched it.

Good point! Actually, I always take the lowest available price into consideration. For classics, it's basically always GOG as it's the only place to geht them. For all other games, I use www.isthereanydeal.com and check the price history to find out the real base price.

Percentages don't matter. I think in $$$ and each game has a certain value in my eyes. If discount makes the final price lower than a number I see fit, it's good discount.
For example, PSN has "deep" sales but its base price for 5 years old game is high, so it doesn't even make me consider a purchase.

My breaking points: $10 for a game I'm interested in but unsure about ($5 for older), $20 for new-ish moderately interesting game, $2-3 for x-th copy of good game.

The price tag is actually more important than the discount for me. There's more chances I grab a AAA titles when it goes on a 75% discount while I buy a full priced indie on release. Overall a 60% discount after 1-2 years on occasional sales seems quite reasonable for me.

I'll go with this ^.

Really, any discount is good.

But considering that we're getting some $40 games (BitD price) for 25% of the original cost or less, there really isn't a whole lot to complain about with today's "full retail" prices. I mean, I'm enjoying the crap out of Deus Ex now - never played it way back when - and 10 bucks seems like a generous price for the 30+ hours of enjoyment I'll get from the first playthrough.

75% off and above.

50% or more is easily good enough for me, any lower than that and I might as well have just bought it full price in my mind.