I'd have to disagree, and say that u can stop all thought, and ur mind will be clear, but practising "samatha" meditation (cessation, or not thinking meditation) is only part of it... I think that the other part of it actually involves lots of thinking, which seems like a contradiction, but bear with me...
as u probably notice, u practise the basic yet effective "not thinking" meditation and there are moments within ur practise when u reach that clarity of mind that ur looking for, even if it only lasts a few seconds or a few minutes, and thats the kind of clear mind ur aiming for...
however, as soon as you start discriminating between this and that, start thinking about looking out the window, start thinking about whats for dinner, etc, etc, ur mind wanders, so ur supposed to bring it back to ur breathing, or the sensation of ur thumbs in the mudra ur using, but in my humble opinion, this does not always work, and it doesn't work because u have not thought enough beforehand...
if, as a buddhist, u've got to the stage where buddhism is no real mystery anymore for u, and because of that neither is the self, and u are comfortable with ur existance, u stop running around chasing ur own tail, thinking all those big and small things that ppl ponder everyday, then the clarity lasts longer, as its got room to grow in...
we all have thought patterns, we think about the same things in the same way, time and time again, and the idea is samatha allows u to stop this... these thoughts have been created by u, inspired by others, the books u've read, the films u've watched, ur culture, etc, etc, and over time they become this character, but its a fake, its a product of all those things u've been exposed to over the course of ur life, so u sit and do the notthinking to give ur mind a chance to break free of these patterns and eventually u can then sit down and work out who u are and what u really think...
equally, once u have got to a point in ur life where there are very few mysteries left for u to ponder upon full stop, again, that mental clarity within ur meditative practise lasts a lot longer...
I think that if there are things that are biting at ur ankles when ur meditating u should contemplate how useful it is to u, how relevant, and instead of trying to force ur mind to be still, u should maybe, in the early stages at least, analyse these thoughts and try to appreciate what they are, and then dismiss them if they are not important thoughts, and just return each time to ur focus, the breath, the tip of ur nose, the sensation of ur two thumbs touching... of course, u are thinking, ur thinking about the thumbs, the nose, etc, but, after a while, distracting urself from ur thoughts works...
also, u have to watch how much stimulation ur getting from external sources- tv adverts, mtv, soap operas, all these things are designed to hook u in and evoke emotions within u, which they do, add a few cups of coffee to that, and ur mind is making connections between A and D and C and G and u have no room for not thinking...
just my thoughts..