Short form periodic table（1869）
This is based on the oldest periodic table, Mendeleev’s table.
Elements with similar characteristics fall in vertical columns. Blank
spaces exist for the undiscovered elements so that certain elements
could be grouped together.
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Long form periodic table（1905）
Unlike a short form periodic table, each period is shown in a
single vertical column. Although relevancies between the 1‐
3 and 4‐7 periods are difficult to understand from this table,
it is easy to understand vertical similarities.
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Janet left‐step periodic table (1928)
This table has a characteristic structure which shows a closer
connection to the order of electron‐shell filling and quantum
mechanics. The form of this table is more congruent with the order in
which electron shells are filled, as shown in the accompanying
sequence in the left margin (read from top to bottom, left to right).
http://en.wikipedia.org/wiki/Periodic_table#Alternative_structures
Pauling style periodic table（1950）
Compared to the long form periodic table, it is easy to
comprehend the relevancies between the 1‐3 and 4‐7 periods. On
the other hand, it is a little hard to distinguish between typical
elements and transition elements from this table.
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Theodor Benfey's spiral periodic table (1960)
The elements form a two‐dimensional spiral, starting from
hydrogen, and folding their way around two peninsulas, the
transition metals, and lanthanides and actinides. Benfey said that
this table shows a beautiful step‐wise periodicity.
http://en.wikipedia.org/wiki/Periodic_table#Alternative_structures