Go and see a dermatologist! That's what I did. If he/she is quite certain that they're not cancerous (which would probably be the case for small flat moles) then they can be removed be laser. What happens is, they put numbing cream on the mole, then use laser to destroy the tissue. Then there's a tiny scab for 5-7 days which falls off. It takes about 8 sessions, which have to be 1-2 months apart. No scar at all and I'm so glad I had it done.
The other method which other ppl mentioned is surgically cutting them off, which leaves a small line scar, and is for bigger and/or raised moles.
And the cancer thing is not true so don't worry! It's actually safer to get moles removed if you think they could be cancerous. They cut it off then send it for analysis to see if it's actually cancer, but it's normally unlikely.
This was all explained to me by my dermatologist. It SHOULD be right.