Yes, I value medals ... but you'd expect me to say that!
Same reasons as Kicked-It - each one represents the miles in training, not just the day itself. It's good to have some kind of memento from an event and I suppose a medal is as good as anything else. They're also practical. I've done over 100 races in the past 10 years and if they'd all handed out a mug or horse brass or T-shirt or mantelpiece ornament I wouldn't have room for them all in the house.
Some I value more than others - the first (Reading Half Marathon 2000), the biggest and heaviest (Indian Queens Half Marathon 2008), and also the full marathons gongs because they stand for the most hard work. But I like them all!
Also, when I was a kid I hated PE and was useless at everything. On sports day I was the one cringeing in the corner of the field. I can't say I've been left psychologically scarred by that, but to be able to turn up to a race, trundle round and finish usually about half or a third of the way down the field makes me feel good. The gong is a small reminder of a morning well spent, usually in a nice place and in good company.