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Last fall, I was approved for two Cap One Platinums (now upgraded to Quicksilvers) and a Quicksilver One when my scores were below 600. Was also approved for a few store cards as well.
Really depends on what you consider good here. Good could mean something thats generally above your scores, something thats overall generally useful like the everyday cards with amex, even the Quiksilver isn't a bad card in my opinion and one everyone who has some dings/new to credit has/should go through at some point. Cap probably defines good as anything that can be swiped so everyones got a diferent opinion.
The Amex everyday is around 660...i think? blue cash i think a bit higher, 670's? Those would probably be my starter defintion of good cards.
I think breaking out of subprime usually happens around there too as a general rule(I could be so so so wrong though).
If you want, google credit pull data base and play around with it. you can punch in your score and the name of a card you like and you'll have a general idea of what scores it takes.
With a EX 675 I was approved for a AMEX PRG, AMEX Gold Delta Skymiles SL1000, and the BCE SL4000 all within 1 month.
I was approved for a CapitalOne QuickSilver One MC (now upgraded to QuickSilver) when my scores were all under 600.
I was recently approved for an AmEx Blue ($1,000) and Chase Disney Rewards Visa ($4,500) at EQ 634, TU 650, EX 616.
Approved for Barclay Ring with $500 SL in 2013 (FICO's were mid-600's)
Approved for FNBO Amex with ~$3k SL in 2015 (EQ FICO was like 649 or something like that, not sure about the other CRA scores though)