Always!
Wearing your seatbelt's compulsory here in Ireland.
Driver along with front and rear seat passengers are legally required to wear one and the driver is responsible for all of his/her passengers. If any of them are not wearing seat belts, the driver gets fined.
It's a 60 Euro (US$76) fixed penalty (you can pay within 28 days online or at the post office).
If you don't pay for up to 56 days, it becomes 90 Euro (US$114).
You also get 2 penalty points* on your driving license.
Alternatively, you can refuse to pay the fixed penalty and opt to go to court. If you are convicted in court, you can get up to 4 penalty points and the fine can be up to 400 Euro (US$508)
You're also required to provide appropriate child seats / restraints and booster cushions and have them fitted in accordance with regulatory requirements for any small children traveling in the car.
Similar regulations apply to taxis, with the only difference being that the passenger can be fined for not wearing their seat belt. However, the taxi driver's responsible for anyone under 18 and he/she will be fined in that case.
Taxis aren't required to provide baby seats.
School busses and most long-distance busses are now fitted with seat belts and where they are fitted you're required to use them. The traffic police occasionally do spot checks and you can be fined for not wearing them. The bus driver's also required by law to announce that passengers must wear the belts.
*The penalty points system applies to 69 driving and license offenses and if you accumulate 12 points your license is cancelled for 6 months and you have to re-qualify after that.
It uses the slogan "Get the point, not the points!"
The fixed charge + points are used for minor offenses. If you're charged with serious offenses like drink driving, dangerous driving (including speeding really excessively), breech of duties at scene of an accident, driving without insurance etc etc you would be arrested, charged and you'd have to appear in court as normal.