I have seen that usually one finds polynomial invariants for oriented links (for example the Jones polynomial, the Hompfly polynomial). Does anyone know what polynomial invariants exist for non-oriented links? Thank you for the help.
Update I have found out that there exists another polynomial, not mentioned in the other answers/comments. It is the BLM/Ho polynomial. One can read the definition in the original papers (Brandt, R. D.; Lickorish, W. B. R.; and Millett, K. C. "A Polynomial Invariant for Unoriented Knots and Links." Invent. Math. 84, 563-573, 1986; Ho, C. F. "A New Polynomial for Knots and Links--Preliminary Report." Abstracts Amer. Math. Soc. 6, 300, 1985) or http://mathworld.wolfram.com/BLMHoPolynomial.html