I have few cracks in my basement that leak water when it rains, what is the best way to solve this problem?

Make sure that gutters and down spouts are clear and working. Install splash blocks at down spouts to carry water away from the house. Better yet is to install piping at each downspout to carry water far away from the house. Check grading to insure that all water can and does run away from the house. Other more drastic measures can be taken but do these first. You may be pleasantly surprised.

It depends on the type of wall that you have.

I'm assuming that the wall is solid, poured concrete from the way you described the problem.

This is a common occurrence in these types of walls. The concrete wall will "cure" and shrink, which causes the cracks. Obviously, this allows a seem for the water to penetrate into your basement.

There are companies that do a "crack injection" process, which seals the wall with a eurethane material. I'm not the biggest fan of this as it is a continual process that needs to be redone.

There is a neat product called Flexi-Span - which truly solves the problem and prevents future cracks from forming due to built-up water pressure. Take a look at it here: Wet Basement Waterproofing - FREE Consumers Guide!.

Actually, the product page is at Concrete Basement Wall Crack Repair - FlexiSpan!

Best Wishes!