Downs syndrome is chromosomal, not mental, as the problem is in the chromosomes not the brain.
Tourettes is a big one, it's not limited to swearing either, the brain just does what is not socially acceptable, so some sufferers say lengthy insults, others make odd noises, some say random words, and the most well known is swearing, it's very distressing for the sufferer.
Autism is the obvious one, but there are many different flavours, I have asperger's syndrome which I would say to myself isn't a mental illness but a personality trait, which leads me to be in denial that there's anything different or 'wrong' with me, I wouldn't be surprised if all autistic people feel the same way, but I do get incredibly upset when I do stupid things that are probably attributed to it (Although I'm still in denial with myself).
There is sequencing disorder, where a person cannot stack tasks in a correct sequence, they tend to forget tasks too, so they might go to the fridge to get a snack, but by the time they start walking their brain thinks getting up is the end of the task so forgets about opening the fridge and getting the snack and the poor person is left confused and frustrated (They can end up going hungry or dehydrating themselves because their brain thinks they have completed tasks).
Some countries don't believe in this one, but in the UK dyslexia is a condition that affects how information is stored, read, or processed, so reading can be incredibly difficult as the brain stacks up all the letters on a page until the person stresses out and throws the book, or with maths where one example could be that they keep a number in their head, but whenever they try to add a number to it they end up forgetting what the original number was so need to write it down.
The UK is very big on dyslexia as any under achievers at school end up getting screened for it, even if it's just laziness or lack of mental nurturing, so a child can end up being labelled as dyslexic when in fact they just don't know the base theory behind what they are doing as their home life never nurtured their need to grown knowledge or perhaps they never read a book or even learnt how to read sentences, which is why some countries deny it's existence, so it's quite sensitive to where you're living to if you're allowed to write about it.
Also, here in the UK the education system treats idiocy as a mental illness, so if someone literally is unable to learn anything at all and is a complete idiot, there's a good chance that the brain hasn't developed properly and that there is an underlying mental illness, some special education targeted schools include this one. There is a correct term for it, I can't remember though, I think it's below percentile achievers or something like that. It goes on medical forms and there are places that help them get jobs, so it's definitely considered an illness in the UK (Ridiculous as it sounds).
Schizophrenia is there too, I know some sufferers of this, they go unnoticed because they don't realise something is wrong with them, there tends to be a history behind it, but you get sufferers who just have it.
Here's a list:
http://en.wikipedia.org/wiki/List_of_mental_disorders