These are websites I use myself. There are many others.

ancestry.co.uk - I am a member of this site. They offer access to the largest collection of UK family history records online, including Census information from 1851-1901, Birth, Marriage & Death indexes from 1837 to the present day and some Parish and probate records dating back to the 1500’s. Much of the information available here can be obtained free elsewhere, but having it all available on one website is very convenient. If you join this site though it is worth pointing out that the quality of their transcriptions from the original enumerators' census forms is variable and maybe not as good as other websites. However, having the original enumerators' forms available to view at a high level of detail more than makes up for the rare transcription errors.

Ancestry.com - similar to ancestry.co.uk, this is the main US based website with fee-based access to the US Federal Census, from 1790 up to 1930. Also, Birth, Marriage & Death records, OneWorldTree and various other resources.

Rootschat.com - "is an easy to use messaging forum for everyone researching their family history or local history. The focus is on Ireland and the British Isles. Local Historians and Family Historians have a great deal of knowledge to share. This service is entirely free, with the hope that you and the historian and genealogy community as a whole will benefit from it."
A large website with message boards for every English, Welsh, Scottish and Irish county as well as other regions such as The Isle of Man. There are also message boards devoted to subjects such as photo restoration, the Armed Forces, one name interests etc.

Old-maps.co.uk - "Providing access to Britain's most extensive digital historical map archive. Find out where your ancestors used to live or check out what your neighbourhood looked like over a hundred years ago."
This website contains an online database of highly detailed digitised 19th century Ordnance Survey maps of the whole of the UK that can be searched by main place name or browsed by county. Moderate quality maps can be printed out and higher quality maps purchased as downloads or ready printed. Very useful to see exactly where your ancestors lived in relation to each other, the detail level is down to individual buildings.

Cyndi's List - of genealogy sites on the internet. A major resource now over 20 years old and sporting over 330,000 genealogy and family history related links.

Rootsweb - "The largest and oldest free genealogy website." A comprehensive website including message boards, mailing lists and family trees. Some of the search facilities need a paid membership to view the results. Also hosted at Rootsweb is -

LDS IGI batch numbers - Index to the LDS (Latter Day Saints) batch numbers for the IGI (International Genealogical Index). This is held on the Rootsweb server and from here you can check counties to see the coverage split by parishes for the area you are interested in. Each parish batch number is calls up a search page hot-linked to the batch of records to allow browsing or searching within that set of records. This index also helps highlight areas missing from the IGI.

Family Search - "The largest collection of free family history, family tree and genealogy records in the world". Run by the Church of Jesus Christ of Latter Day Saints (LDS). They produce free family tree software called 'Personal Ancestral File', along with an associated reporting program called 'PAF Companion', both of which I use. These possibly do not have as many features as some other paid-for software but are likely to be very well supported in the future. They also offer free access to the IGI (International Genealogical Index) containing (for the UK) millions of details transcribed from parish records. These records are very incomplete and patchy in coverage but are still a major internet resource.