Since Diablo III is fully dependent on gear scaling, all 5 classes have an equal chance to be successful in Hardcore. It all comes down to your own play style and the amount of patience.
Having said that, some classes may do better than others in certain scenarios and/or under certain circumstances. For example:
A tanky Barb has higher chances of survival in case a DC occurs. This is also true for classes who invest heavily in Life Regeneration gear, opposed to gear with a lot of Life on Hit.
I often read that a Monk is known for the healing skills but did you know you that a Witch Doctor can excel in healing through skills with DPS just as well?
As always Dazzed is right. Barbarian will give you, i think, the easiest way until act I inferno. Monks are very viable and will become even more worthy starting act II inferno. Wizz, well ... They are wizz, with the right sets of skills and some actual player-skill they are great. Crazy escape skills and very nice dmg.
Dh are pretty risky to play here but, if you are good at positionning and aiming, they rule over dps without any doubt. Still an error will cost you your life tho, so choose wisely !
As for WD, i think they are currently the hardest class to play in HC. In my opinion, they globally need a bit of a up, as they take a lot of damage, and lack a little dps. So they are actually, i think, the best challenge.
Hope it'll give you some ideas.