LEO:
Shakesperean (also:) Shakespearean (adj.) - shakespearesch (auch:) shakespearisch
Shakesperian (also:) Shakespearian (adj.) - shakespearesch (auch:) shakespearisch

Chambers:
Shakespearean or Shakespearian
http://www.chambersharrap.co.uk/chambers/feat...

Concise Oxford:
Shakespearean (also Shakespearian)
http://www.askoxford.com/results/?view=dict&f...

M-W (same as Webster's 3rd unabridged):
¹Shake·spear·ean
Variant(s): or Shake·spear·ian
also Shak·sper·ean or Shak·sper·ian
http://www.m-w.com/dictionary/shakespearean

NOAD:
Shakespeare, William - ...
–DERIVATIVES Shakespearean (also Shakespearian) [n. & adj.]

Random House unabridged:
Shakespearean ... Also, Shakespearian.

OED:
Shakespearian, a. (and sb.) Also Shakespearean, Shakspe(a)rian, -ean.
The forms in -ian are alone correct according to the relevant analogies. The other variations follow the diversities of spelling of the poet's name. The spelling Shakspere, adopted in the first edition of this Dictionary, was advocated by Sir F. Madden on the ground of the signature in the poet's copy of Florio's Montaigne, and accepted by Dr. Furnivall and the New Shakspere Society; the standard form is now Shakespeare.

Fowler/Burchfield:
Shakespeare. Now universally spelt thus but in the early decades of the 20c. Shakspere was the more usual form, and was recommended by the OED (1913) and by Fowler (1926). The corresponding adj. (and noun) may be written as Shakespearian (thus in the house style of OUP) or Shakespearean (in The Times).

Garner:
Shakespeare; Shakespere; Shakespere; Shakspeare; Shakespear. Although each of these variations has appeared at one time or another in scholarly writing, Shakespeare is the standard spelling.
Shakespearean; Shakespearian. The first spelling is standard AmE, the second a primarily BrE variant. On the merits, Shakespearean is preferable because it preserves the final vowel in the great bard's name. Cf. Euclidean & Mephistophelean.


web hits:
+Shakespearean - 2,820,000 (GooBooks 4,450, GooSchol 25,600)
+Shakespearian - 637,000 (GooBooks 2,930, GooSchol 6,880)
+Shaksperean - 633 (GooBooks 790, GooSchol 188)
+Shaksperian - 889 (GooBooks 917, GooSchol 276)
+Shakesperean - 42,800 (GooBooks 806, GooSchol 216)
+Shakesperian - 35,100 (GooBooks 841, GooSchol 301)

No idea where these entries in LEO came from, but the preferred, standard modern spelling is definitely 'Shakespearean,' as the dictionary consensus and the web hits show.

The only other variant accepted in most dictionaries is 'Shakespearian.' The OED, oddly, still preferred that one when its entry was written, but I suspect that even then it was a rather eccentric editorial decision and they were already well behind the curve (and protesting too much, from the tone of it). They don't even say what analogies they're referring to, and the unsupported claim really does seem a bit perverse, since other English writers whose names end in silent E are -ean as well: Joycean (James), Blakean (William), Burkean (Edward), etc. But in any case, more recent Oxford dictionaries no longer seem attached to that view.

All the other spellings I personally would consider obsolete and/or rare and would not list them at all without that marking.

In particular, most of the modern-day web hits for the last two, the 'Shakesper-' ones, are surely just typos or misspellings. (Remember 'definately' and 'im Vorraus.') Most of the rest, in Google Books and Google Scholar, will probably prove to be books from at least 75 or 100 years ago, or citations for them.