I would like to know the difference between Distant (D) NOTAMs, Local (L) NOTAMs and FDC NOTAMs in the US. Is their meaning obsolete or still in use by the FAA?
Short answer: D NOTAMs are about airports and navigation facilities; FDC NOTAMs are about airspace, procedures or regulations; and L NOTAMs don't exist any more (unless you're in the military).
The information on NOTAM types is a bit messy and inconsistent, to say the least. The Alaskan FSS lists 11 types; the PHAK 13-3 lists 3 types (as acpilot mentioned in his answer); the AIM 5-1-3 lists five in its NOTAM section, plus GPS NOTAMs in the GPS section.
Anyway, here's what the AIM says about D and FDC NOTAMs:
NOTAM (D) information is disseminated for all navigational facilities that are part of the National Airspace System (NAS), all public use airports, seaplane bases, and heliports listed in the Chart Supplement U.S. [...] NOTAM (D) information includes such data as taxiway closures, personnel and equipment near or crossing runways, and airport lighting aids that do not affect instrument approach criteria, such as VASI.
FDC NOTAMs. On those occasions when it becomes necessary to disseminate information which is regulatory in nature, the National Flight Data Center (NFDC), in Washington, DC, will issue an FDC NOTAM. FDC NOTAMs contain such things as amendments to published IAPs and other current aeronautical charts. They are also used to advertise temporary flight restrictions caused by such things as natural disasters or large-scale public events that may generate a congestion of air traffic over a site.
According to the Alaska FSS page, NOTAM(L) doesn't exist any more for civilian use:
NOTAM (L): A NOTAM given local dissemination by voice and other means, such as telautograph and telephone, to satisfy local user requirements. This type of NOTAM is now used only in the military NOTAM system. All NOTAMs previously considered NOTAM (L)s in the civil NOTAM system are now considered NOTAM (D)s.
That's confirmed by AIR FORCE INSTRUCTION 11-208 (I), which describes NOTAM(L) as a military type:
18.104.22.168. Local NOTAM (L series). Local NOTAMs are non-critical and non-safety related information that is essential for the flying and support communities to know. Facility managers may establish the parameters for local NOTAM determination.
Civilian L NOTAMs are now D NOTAMs that start with the specific facility code. You can find them on the civilian NOTAM site, e.g.:
!LOU 05/077 LOU RWY 15/33 CLSD 1605091213-1606222000
And to address your final point, NOTAMs are not obsolete. There needs to be some way to inform pilots about temporary changes or things that happen at short notice, and that's what NOTAMs are for. Many people feel that the system could be improved somehow - pulling up the NOTAMs for even a short flight can give you dozens of results - but there's no doubt that it's needed. Reviewing NOTAMs is an important preflight step, and examiners often test you on it during checkrides. There are plenty of NTSB accident reports that mention NOTAMs, usually in cases where the pilot didn't review them.
A really great source for these kinds of answers is the Pilot's Handbook of Aeronautical Knowledge, or PHAK. You can dowload it for free from the FAA here.
The answer to your question from chapter 13, pages 13-3 & 13-4 of the PHAK:
NOTAMs provide the most current information available. They provide time-critical information on airports and changes that affect the national airspace system (NAS) and are of concern to IFR operations. NOTAM information is classified into three categories. These are NOTAM-D or distant, NOTAM-L or local, and flight data center (FDC) NOTAMs. NOTAM-Ds are attached to hourly weather reports and are available at automated flight service stations (AFSS) or FSS.
FDC NOTAMs are issued by the National Flight Data Center and contain regulatory information, such as temporary flight restrictions or an amendment to instrument approach procedures. The NOTAM-Ds and FDC NOTAMs are contained in the NOTAM publication, which is issued every 28 days. Prior to any flight, pilots should check for any NOTAMs that could affect their intended flight.
NOTAM-D information includes such data as taxiway closures, personnel and equipment near or crossing runways, and airport lighting aids that do not affect instrument approach criteria, such as visual approach slope indicator (VASI). NOTAM-D information is distributed locally only and is not attached to the hourly weather reports. A separate file of local NOTAMs is maintained at each FSS for facilities in their area only. NOTAM-D information for other FSS areas must be specifically requested directly from the FSS that has responsibility for the airport concerned.
NOTAMs are far from obsolete. They are critical and pilots are actually required to familiarize themselves with all applicable information before each flight. NOTAMs are arguably the most important vehicles to help pilots satisfy that requirement.
The civilian NOTAM-L has been discontinued snd evetything that one qualified as a -L is now -D.