These are my favorite internet resources for researching in Illinois, Ireland, and Puerto Rico. There are SO MANY resources out there and I have used many, but these are the best ones for my individual family research.
FamilySearch.org – free and provided by the LDS church
Ancestry.com – best for connecting to other users’ family trees; been a user since 2003 but lately I’m becoming disenchanted with this company
MyHeritage.com – Ancestry.com’s focus for overseas is the UK, mainland Europe, and Scandinavia; MyHeritage.com seems to have a broader international audience with user-submitted family trees
Genlighten.com – I love this site which connects you to people who offer look-up services in the localities of your ancestors; the providers are available to visit their local record repositories, libraries, cemeteries, etc.; this site is free to join and you pay the individual for their services
Illinois State Archives Database – these are only indexes for records and show vital information like name, the date of the event, and the record number in order to purchase a copy of the record itself; orders are processed by volunteers and may take a few months, so be patient
Cook County Genealogy – instantly download vital records from Cook County, Illinois; I use this site for newer records that are not available from the Illinois State Archives, but it is not comprehensive so some records in the time period offered that I look for are not always found at this site
Irish Family History Foundation – RootsIreland.ie has revamped the way they require users to search and view trancriptions of records; recently, some transcribed records include links to a microfilmed image of the actual record!
Placenames Database of Ireland – has both the Irish and English versions of the place names and includes street names
Enciclopedia de Puerto Rico – history of the island as well as histories for each of the municipalities
Puerto Rico En Breve – a lot of general information about the history of the island
Municipality of Peñuelas – not a huge place compared to other metropolitan areas in Puerto Rico; this website took a long time to get fully developed and now it has current information as well as a section about the history of Peñuelas
Catalan to English Dictionary – not a complete dictionary for the full Catalan language, but works well for most general vocabulary words