Yes, the mother's diet definitely affects the child.
My own family's experience is that what you eat makes a big difference. Some infants are very sensitive to onions (gives the baby gas), or spicy food, or coffee/caffeine, or even cow-milk products.
However, the general advice is to continue eating your regular diet and see how that works, before you change anything in the diet -- chances are that the baby will be fine. Only if there are problems (stomach aches, gas) should you consider changing the diet.
Regardless what your diet was before the pregnancy, just make sure that you get enough vitamins and minerals while pregnant and while breastfeeding. Also, listen to the body: if you crave something in particular, it's probably not a coincidence.
A quick Google search reveals these articles that seem good:
(I know -- I need to summarize the linked articles. I will do so later.)
Alcohol goes straight to the milk, so breastfeeding mothers should avoid it. However, it's probably all right to sip a little red wine for instance because ½ glass of red wine won't give you a significant amount of alcohol and the amount that arrives in the milk is a minuscule fraction of that. So it's best to abstain, but don't freak out over it.
Coffee/caffeine takes 3-5 hours to work. Don't ask me why it's slower than alcohol; this is not a science website :-)