Clear gutters regularly. They will tend to accumulate leaves and soil. If left too long you may even find plants growing in them. This will stop the flow of rain water which will overflow.

Prevent leaves getting stuck in the down pipes by placing a downspout leaf strainer in the top of the down pipe. Clean this regularly and you should have no problem.

Alternatively install a gutter guard or mesh which covers the whole of the gutter
Checkout

Cracked gutters may be temporarily repaired with roof and gutter sealant, a thick water proof bitumen mastic.

An alternative is to use gutter repair tape. Checkout Sylglas who supply this. They have a very useful site where you'll find instructions on how to use it as well as other water proofing products for roofs, skylights, flashings, and more.

http://www.sylglas.com/index.htm

Gutter tape. Wrap it around a crack or lay it along the inside of the gutter(must be clean and dry first)

If your gutters are are too bad you may have to replace some parts. Modern plastic gutters are very easy to repair as they are assembled from parts which simply clip together and attach with plastic fixing brackets. This makes it fairly straightforward to remove and replace any damaged sections. The joining pieces have integral rubber seals which form a water tight joint against the gutter sections.

NB WARNING Working at heights can be dangerous. You must ensure that you use appropriate access equipment. It is your responsibility to ensure your own safety.