"Somewhat ironically, I understand that those that haven't paid a bean may well get more than somebody who has fully contributed (natch)."
Yes that's almost true (they would not necessarily get more, but certainly almost the same). Somebody relying solely on the State pension (who may not have made any contributions at all) is guaranteed a minimum income of £163 per week (£248 for a couple). If the State pension to which they are entitled is less than this they can claim "Pension Credit" to take them up to that amount.
The current basic State Pension (for those on the "new" scheme) is £164 per week. This means somebody with 35 years (thanks for the correction, ubasses) who may have paid many thousands in contributions will get £1 a week more than somebody who had contributed zilch. Many drawing their pension under the old arrangements receive considerably less than that (even having made perhaps almost 50 years NI contributions). It gets worse. If a person was a few years short of the required 35 his pension will be reduced pro-rata and if he has additional income (say an occupational pension) that takes him above £164 a week he will not be eligible for pension credit.
So, no, as DeskDiary contends, for many people the State Pension is not a "pension" in the true sense at all but simply a benefit paid at retirement age. That is why, when the government states how much "State Pensions" cost the taxpayer they should only include the pensions that are paid to people who have fully funded them. That is, those people who have made sufficient NI contributions (in £££s, not "years") to fund the payments they receive. All the rest are welfare benefits.
See how easy it is to start me off! :-)