Taken from GURPS Bio­tech.

Any truly alien life forms will not share the same details of DNA, RNA, and amino acids as Earthly life. (The main excep­tion is if ter­res­trial and extra­ter­res­trial life share a com­mon ori­gin, which is intri­guing in itself.)

An alter­na­tive bio­che­mis­try can be based on any of seve­ral differences:

• Chi­ra­lity is the “han­ded­ness” of the many bio­lo­gi­cal mole­cules that come in two dif­ferent and incom– patible shapes. Ter­res­trial life uses only one chi­ra­lity. Life that uses the other may seem very simi­lar, but will be mutually incom­pa­tible (and indigestible).
• Alter­na­tives to DNA can encode gene­tic infor­ma­tion using slight variants (dif­ferent base pairs) or com– ple­tely dif­ferent mole­cules. One example is poly­sac­cha­rides – bran­ching chains of lin­ked sugars.
• Addi­tio­nal amino acids from the over 500 dis­co­ve­red so far could be added to the mere 20 that ter­res­trial DNA uses.
• Sili­con and metal­lic che­mis­try could poten­tially pro­duce enough com­plexity to fos­ter life at tem­pe­ra­tures where these ele­ments are mol­ten, inside tec­to­ni­cally active worlds. (addition: we recently dis­co­ve­red arsenic-based life!)
• Neu­tro­nic com­pounds such as those found on the sur­face of a neu­tron star might form nuclear che­mis­try capable of nur­tu­ring the emergent com­plexity of life.
• Since nuclear reac­tions are rapid, such life would evolve incre­di­bly quickly.
• Magne­tic vor­tices in plas­mas such as stel­lar atmos­pheres or around large pla­nets could concei­va­bly form into self-sustaining and evol­ving sys­tems. “Gene­tic” infor­ma­tion could be enco­ded in tight bunches of magne­tic fields. This is not as far-fetched as it sounds; we do it our­selves in our computers.

And this doesn’t not even take into consi­de­ra­tion (digi­tal life or meme­tic life)!

See also Wiki­pe­dia — Hypo­the­ti­cal types of biochemistry