One of the hinges on my DS Lite is broken.  My DS now opens with too much ease.  Is there any way to repair this?

Not that I know of. Is it the original white DS lite. If so, I have the same problem.

Apparently it's quite a common problem (I found this out after mine went the same way) and I'd heard word you can get in contact with Nintendo's service centre to get it fixed. Personally, mine's not so bad as to be unusable, so I'll live with it until it gets worse or I get hold of a 3DS.

It sounds like Nintendo has been pretty good about these hinge crack problems, so if you call up Nintendo they'll probably do something for you. 

Do what I did.
 

duct tape!

It's a black DS Lite.  I thought about using Krazy Glue, but then thought about the fact that it wouldn't be able to close.  I will give Nintendo a call then.  I just had my doubts since I it's about four years old.  I like having my GBA slot (despite not having played a GBA game in years, and still having two GBAs: NES Special Edition, black).  I'm going on a road trip later this week, so I'll have to send it off in the last week of July.