Money laundering is anything that turns illegally acquired cash into seemingly legitimate funds. People do this because they are worried about the physical security aspects of having that much cash on hand, or would like to make a purchase where cash won't be accepted (eg house, car, stock).
I think real money laundering using bitcoin would be hard right now -- most current methods work by piggy backing on a real business, and just inflating earnings. (For example, you might buy a laundromat and then add +50% income from your dirty money, making it look legitimate to an auditor). As it stands now, after you'd transfered the illegal money, you'd still have some awkward questions about where you'd gotten it from if/when you get audited. (Perhaps someone with more experience can comment here, but it seems bad to me).
Re: illegal transactions, I think the biggest kind of illegal activity that bitcoin makes easier is illegal digital goods / services (eg, corporate espionage, buying bulk stolen credit cards, etc). This is because using bitcoin means you don't have to worry about masking your physical location or banking details from your counter party (basically the same reason people used liberty reserve before it was shut down).
I'm sure one day bitcoin will be used for larger scale money transfers, but right now it just wouldn't make sense to move cartel levels of cash (eg 100 million+/wk) through bitcoin -- that's just too high percentage of the network's total volume to be feasible
(mtgox volume is currently something like 20 million USD/wk)
That, and the potential for tax evasion, of course.