These are the scriptPubKey's that are standard, arranged in order of popularity:

1. P2PKH (Pay to public key hash)

        OP_DUP OP_HASH160 <20 bytes of public key hash> OP_EQUALVERIFY OP_CHECKSIG

2. P2SH (Pay to script hash)

        OP_HASH160 <20 bytes of script hash> OP_EQUAL

3. P2PK (Pay to public key)

 This is now mostly unused, but there are still unspent outputs in the form:

        <33 or 65 bytes of public key> OP_CHECKSIG

4. m-of-n bare multisig

 Also pretty rare.

        <m> [n <public key>s] <n> OP_CHECKMULTISIG

>Should I implement more sophisticated script parser which can detect "non-standard" scripts as well?

No. It's a waste of development time, when nobody uses transactions like that. It's also going to be very difficult to implement correctly. If you don't do it correctly, then you'll think you have coins when you really don't. For example, the transaction:

    OP_DUP OP_HASH160 <20 bytes of public key hash> OP_2DROP OP_CHECKSIG

...is spendable by *anybody*, not just you. But does your script parser know that?

(Note that OP_EQUALVERIFY has been replaced by OP_2DROP in this example.)