10 years. If you have a bankruptcy, it is technically on your credit report for 10 years. After 10 years its like it never happened. However, you can start "rebounding" about 2 years after. I have actually seen credit scores go up after bankruptcy if someone was 6 months behind on everything.
7 years. After 7 years collections/judgments, etc. fall off like they never happened. My bank officer told me that they ignore $5000 in medical collections, because that doesn't really show a intent not to repay, you got sick. But applying for a CC where everything is automated, your score is going to take a hit.
2 years. Late payments don't really count against your score after two years. So if you were 30 days late this month, and caught it up next month, in June of 2015, the drop in score wouldn't be there.
Also 2 years, but not as big of a deal - Inquiries. Stop applying for shite. Score drops 3-5 points for each inquiry. After 2 years, they don't count against you, although after a year there is a gradual increase.
If your score is in the 500s, get current, stop doing stupid shite and after 2 years or so you can be in the mid-high 600s and get approved for most things. After 4-5 years you can be in the 700s.