I have nothing against a high-mileage bike. A well-looked after bike that's done 100K miles will be in better nick than a bike that's done 10K miles and has been abused. Yes, I know I'm stating the bleeding obvious.
My 125 was a 2004 that had only done 9K when I got it in February. And loads went wrong. I ended up spending as much as I paid for it (£2,200) just to keep it going! Tyres, brakes, you name it, it went. It had had unkind previous owners, I'm sure of it. I traded it for the Fazer 600 I now ride after a scare where I thought the main gasket had gone on one of the cylinders. And I'm convinced the gearbox was on its last legs to boot.
The advantage of high-mileage bikes is greater for people like me: undergrads at Uni with little to no money. By only spending money on it when I need to (yeah, right!!), I keep costs down. Cheaper to buy, cheaper to insure, and it gets me into Uni just as well as that bloke's 2-month old GSXR750. His is shinier though!
On a more cynical note, an older bike is especially good if you crash (if you're more than a bit stupid, as I am, you will). If the van that reversed into me, knocking me off a few days ago had hit the Gixxer... To say there would have been a lot of tears would be an understatement! And yes, bike and I are fine. Just a few more scratches to the already scruffy front fairing. Which I intend to repair completely and re-spray when I get home anyway.