Here is an overview of all BASF brick versions I know.
Top row
BASF C1-C4
Pat. Pend. Scratched C and number 1 to 4.
Update: These bricks come in two versions. The oldest version has 3 identical tubes, the newer version has a different middle tube.
Second row
BASF Mold pip edge
Pat. Pend. Number on the short side.
They look similar to the BAYER old logo, but the orientation of the mold markings is different. They also sound different.
Numbers 1 to 20.
Third row
BASF Mold pip stud
No markings inside
The white brick has a black dot on one of the tubes.
This is a burn mark (black or brown burnt areas on the part located at furthest points from gate or where air is trapped) caused when the mold lacks venting or the injection speed is too high. Such burn marks are found on BASF bricks more often. [See this page]
First phase: no markings, but a line and a cross inside the center tube of two of the bricks.
Second phase: Roman numbers I to X [See this page]
Fourth row
BASF Number only bricks
Number above the right tube.
Numbers: 5, 8, 9, 10, 15, 16, 17, 18, 19, 20, 21, one brick Pat. pend with only “Pat.” erased and four different Pat. pend bricks, on which both “Pat.” and “pend” are erased in slightly different ways (16 bricks total).
[See this page]
Also “pat. pend,” erased bricks that are probably related. Found mixed with the number only bricks in the same colors. Two versions exist. One were the “pat” is erased and the “pend” is not, and a brick were both are erased. The brick with both not erased has not yet been found.
The number only bricks were found mixed with V-bricks.
Fifth row
V-bricks – third phase with solid studs
Pat. Pend, a number and V.
Some number 40 bricks have a broken tube.
Numbers 1 to 6, 8 to 11, 13 to 16, number 40 (replaces 12) and a brick without markings (replaces 7)
[See this page]
Sixth row
V-bricks – second phase with hollow studs
Pat. Pend, a number and V.
Numbers 1 to 11, 13 to 16 and number 40 (replaces 12).
[See this page]
V-brick phases (fifth and sixth row)
First phase – numbers 1 to 16, open studs. Used in LEGO production, I am not sure if it was used by BASF. We would need to find a set in an odd color including number 12.
Second phase – open studs, only number 12 replaced with number 40.
Missing intermediate phase? – MAYBE there was another open stud phase where both number 12 and 7 have been replaced. It has not been found yet. We would need to find some identifiable BASF V-bricks with a matching brick without markings with open studs. It is also possible that there was an earlier closed stud phase. We would need to find a number 7 with closed studs to identify that one.
Third phase – Closed studs. Number 12 has been replaced by 40 and number 7 has been replaced by a brick without markings.
[Original post and comments on Flickr.]