WARNING – DO NOT UPDATE TO OS 3.1.3 BEFORE YOU HAVE READ THIS
By all accounts the new 3.1.3 provides no real benefits but will kill your chances of jailbreaking if you are on an iPhone 3GS or iPod touch 3G (or iPod touch 2G with MC serial). It also contains a new baseband that has not been hacked and so if you need to unlock your iPhone 3G you should avoid upgrading.
Blacksn0w has not been updated and does not work with 3.1.3 but the ever industrious Dev-Team have made a few tweaks to their recently released redsn0w 0.9 tool so that it will jailbreak OS 3.1.3 on iPod touch 1G, older models of the iPod touch 2G, iPhone 2G and contract (no unlock required) iPhone 3G.
If you’re a 3GS owner then you need to make sure you have backed up your ECID/SHSH signatures through Cydia or Rock to ensure that when Apple stop signing the 3.1.2 firmware you can restore or downgrade to 3.1.2 if required.
Update/ 3.1.3 jailbreak guide HERE