Well there's a lot of people trying to be helpful here, but not too much it gets at the truth - HC's contributions being a notable exception.
So what's the truth?
Assuming you don't reach 60 (as a woman) by April 2010, you can't draw your basic state pension at 60.
There is then a rising sliding scale by which women can draw their basic state pension between April 2010 and April 2020, such that every woman not reaching the age of 65 before April 2020 has to work until 65 before getting the pension. If you fit into this bracket and post your age, I'll tell you when you can draw the pension.
After April 2010, you will only need 30 qualifying years to entitle you to get a full basic state pension, but the bind is you just can't stop paying the NI contributions when you've got to the 30 years. You unfortunately have to keep paying them until you reach pensionable age - if, and only if, you are working and earn enough to exceed the threshold (about 3100 per week right now). So until you are living off other earnings, you are stuck - you have to keep paying the NI. It's called swings and roundabouts - some people gain, others lose out.
As HC has pointed out, in addition to the basic state pension, you will almost certainly be entitled to an additional pension based on your earnings level (unless you were contracted out and in a private pension scheme - and it seems you weren't). This is based on your earnings (because you will have paid more NI if you had higher earnings). It is this that you can get the pensions forecast from the Pension Agency. It has had various names over the years, including the Second State Pension, SERPS and the Graduated pension (if you were earning before 1974). They will also confirm the number of qualifying years you have for the basic state pension.
I hope that gives you a more complete picture than the mish-mash of stuff you've received so far.