Travel Cheques are a big advantage over carrying cash. If you lose them somehow or they get stolen, they can be replaced (compare that to cash, if you lose cash you won't get it back!)
There's more security -- as your signature is needed... once you get the cheques you will be asked to sign in the lower right line, and when you 'cash' them you do it in front of the cashier so they can compare signatures to accept.
Travel cheques are widely accepted.
I recommend getting them from AAA if you're a member, they don't charge extra fees like some banks do.
I can't think of any cons about travel cheques... except for really stupid cashiers who have NO CLUE what they are... if that's ever a problem, talk to the manager and they'll know what it is. Like duh.