Most (all?) of the agencies which originated in the US began using US Navy tables.
NAUI & YMCA use modified US Navy tables. They've backed off the NDL's various amounts.
YMCA will tell you they backed off the NDL's 2 letter groups, but that's not exactly the case, although what they did was very close. They backed off 2 letter groups for all depths except 100 ft. At 100 ft, they backed off 2 letter groups and 2 minutes. They then left the repetitive group as if they've backed off three letter groups. I don't know why, but I suspect it may be because backing off 2 letter groups at 100 ft would have left the NDL's at 100 ft and 90 ft identical and that would have seemed odd. Now this seems like an error on the side of caution, but in actuality for dives to 100 ft for 16 - 18 minutes, the YMCA tables are less conservative than the US Navy tables. Those times at that depth on the US Navy tables leave a diver in the F repetitive group. On the YMCA tables the diver is in the E repetitive group. Except for those three minutes at 100 ft, YMCA tables are the same or more conservative than US Navy tables. I have pointed this out to the YMCA SCUBA Program. They feel it is an insignificant difference.
NAUI tables are backed off 3 letter groups for 40 ft, 2 letter groups for 50 ft, and 1 letter groups for all other depths. NAUI also increased the time to clear the tables from 12 to 24 hours.
MEDA uses straight US Navy tables, but did make them harder to read.
PDIC uses straight US Navy tables in the exact same format as those published by Jeppesen.
DCIEM developed their own tables based on slightly different theory. The format is much more user friendly.
PADI switched from the US Navy tables to their own in the late 1980's. It may have been the result of several product liability lawsuits of the time. ABC news did a story on it in, I believe, their 20/20 program. I taped it, but I have not been able to find that tape. In my opinion, PADI got a raw deal on the program. ABC interviewed people who were bent while pushing the tables to the max (I was following the interview with tables in hand) and then asked PADI why they were bent while "well within the limits" of the tables. They also gave PADI a hard time for continuing to sell their version of the US Navy tables when their "newer safer" table was available. What struck me as odd was they accepted as a given that the newer table was, in fact, safer with no evidence to support the claim. If memory serves, the people interviewed in the program would have had longer bottom times had they been using the newer tables. Bottom line, don't push any table to its limits.