What you want is the Satellite Catalog or "SATCAT" file. The original public source for this is the Satellite Situation Report (SSR) published daily on Space-Track (http://www.space-track.org - free registration required).
This file contains a record for every catalogued object which includes the launch date, launch site, object name, etc.
Here's a typical record:
1957-001B 2 CIS 96.1 65.0 945 227 N/A
SPUTNIK 1 Launched (10/04/1957) Decayed [01/03/1958]
Breaking it down...
1957-001B - International Designator, 1957 is the launch year, 001 indicates that this was the first launch of that year and B indicates it was the 2nd piece from that launch (A was the upper stage, which also achieved orbit)
2 - The object catalog number, aka NORAD id
CIS - Responsible country or organization, in this case the Commonwealth of Independent States, AKA Soviet Union. Space-Track has a key for these abbreviations
96.1 - Orbital period in minutes
65.0 - Orbital inclination in degrees
945 - Apogee altitude in Km
227 - Perigee altitude in Km
N/A - This position would hold the RADAR Cross Section (RCS) in m^2, but it's not available for this object
SPUTNIK 1 - Object common name
Launched (10/04/1957) - UTC launch date
Decayed [01/03/1958] - UTC decay date
I just noticed that the SSR doesn't have the launch site in it - I guess that's only in a separate SATCAT data product, which isn't available for general users on Space-Track. The information is available via the site, but not as a file.
Several of these fields may not be available for every object (inclination, period, apogee, perigee, RCS) but the launch date and international designator is always there.
A few other things about the SATCAT...
SATCAT records for an object aren't static - they are updated as orbits change or decay. So the current inclination, apogee, perigee tell you where it is now, but not where it's been. You would need the SATCAT or TLE history of the object to understand that.
Debris objects can be correlated to the original object via piece component of the international designator. This is also true for objects deployed from other objects.
Objects which don't remain in earth orbit have a note to that effect in place of the orbit shape/orientation parameters. Here an example:
1969-059A 4039 US CIRCUMLUNAR N/A
APOLLO 11 CM (COLUMBIA) Launched (07/16/1969) Decayed [07/24/1969]