Not all of the sites I have listed are free to view records but if you do get a hit on one of the sites, and feel that it is deffinately the right person then by all means, put a little money into your searching and view the recrod.
If you are wanting to search passanger lists then have a browse of these sites:
www.findmypast.co.uk – this is a website where not only can you research your ancestors, you can also put your family tree on this site and have others view it much the same as you can on ancestry.co.uk
www.coraweb.com.au/shipindex.htm – this one in particular is very helpful as it lists many other sites which helps you to locate the right year, ship and even location and much much more, certainly worth having a look at.
Looking for a convict then the following sites should be of some help.
www.convictrecords.com.au – lists the years and ships which sailed to Australia, how many passangers, average sentence and life sentences and also roughly when the ship arrived. Also on this website you can find the names of the convits and where they were convicted. This information is free and a helpful stepping stone, if you know the name you are looking for and the location then this site will help you piece together the rest of the information.
www.nationalarchives.ie/search/index.php?category=18 should help if you have an Irish convict in the family.
Still a little stuck, then try Criminal Registers
www.oldbaileyonline.org makes for very good reading, provided you know the name of the offender then you should have a pretty good chance of finding his court records and all that goes with it. You can search records from 1600s-1900s
http://www.sl.nsw.gov.au/research_guides/convicts/instructions/crim_reg_ancestry.html Another good site full of information on court records.