These are not 100% reliable (Although 95% of the time they're correct) and free!

-To check NCT expiry (This will also tell you the last NCT Center location)
Go on NCT.ie , Click bookings, Then click the little 'Click Here' under the blue Book Your NCT or Re-Test

- NCT/Tax and number of previous Irish owners, (Not always 100% correct)
http://www.carsireland.ie/add.php

- NCT/Tax, Adverts.ie mobile app go to place an ad for a car and input the Reg in should autofill Tax/NCT.

- Motortax.ie, 'Vehicle Transaction Enquiry' Will show if a car has had a change of owner or replacement logbook within the last 3 months.

- https://www.gov.uk/check-mot-history
For checking UK MOT history (Also shows mileage from 2011!)

Then the paid ones are:
Mywheels.ie
Cartell.ie
Motorcheck.ie
Hpifirst.ie
And many more.

Interestingly cartell are the only ones to show my Sierra as an RS Cosworth, Other checks say model Unknown. (Whether it means anything or not I don't know)