What is the best way to remove limescale around the water rim in the toilet bowl?

If its just a limescale I'd try Limeaway or CLR but most toilet bolw cleaners used weekly should be sufficient for toilet cleaning.

If things are really caked on, then using the liquid chemicals as described above and an abrasive of some kind like #00 steel wool or pan scrubbers can also be helpful.

I have had a similar problem and found that using a pumice stone worked without scratching my toilet bowl.

The one thing you do not want to use in your bowl is any acid, such as Muriatic . I can not advise against using muratic acid, or any acid, in a enclosed area such as a rest room strongly enough. As a young boy I would take limed up toilet bowls out in the alley behind the shop and boil the lime out of them. Over half a century later my lungs still carry the scar tissue that the acid fumes caused. A few years ago I lost a good friend when he used a commercial drain cleaner containing sulfuric acid in a unvented bathroom. Acid IS NOT A GOOD IDEA to use to clear mineral buildup. Take it from one who's paid the price. Regards, Tom

Tom is oh so correct. Muriatic acid is actually a dilute form of hydrochloric acid and a few whiffs even outside can buckle your knees. I use it to clean my boat hull since it has not effect on fiberglass but eats the crud. I can only do this with a big fan or on a windy day.

Click on the links below it may help you

How To Clean A Toilet (DIY & Home: Bathroom Cleaning)
How can you remove limescale from a toilet without using chemical products? - Yahoo! Answers

An interesting post of ideas from other readers like us. The "Non-chemical" suggested by nearly all posters is vinegar which is an acid, milder than Muriatic but an acid none the less. Limeaway is also an acid, phosphoric acid stronger than vinegar milder than muriatic.