I agree with many of the proposal for trading, particularly limiting the number of trade routes to a cap for the entire cilvisation, say ten. This is agnostic to tall or wide Civs, rather than encouraging city spam, as has been stated by many here.
I should just state that I don't mind the management of trade routes and think they add a lot to the game, but I agree they are too powerful as it stands and need reducing in strength.
But could I also propose a few additions (I don't know if Civ5 already has these as I've not played it):
1) Given that routes are capped at say 10 per civ, create a new National Wonder, say 'Trade Nexus' that grants 3 or 4 additional trade routes to the one city in which it is built. This is only possible after researching an expensive tech, but turns that one city in your empire into a true hub for trade. With 4 added routes, it's nice to have, but not essential and its more a mid-game building.
2) Remove the ability to render your trade caravans immune from alien attack, but have such attacks reduce the returns rather than kill the convoy outright (some of the convoy get killed but the route remains) - this forces you to protect your trade convoys with military on the route, but not to be constantly rebuilding trade units to replace dead ones. You might make longer routes more profitable to make them worth your while. For sea trade this reduced return would only make sense if the unit was a fleet not a single vessel(!)
3) Add an option to diplomacy to cease trading with a given civilisation. This not only severs your trade with them, it prevents them from setting up routes to you (which you currently have no power to prevent unless you're at war). You can then stop helping the guy whose pulling away from you in affinity, without attacking him. Removing the trade embargo could be an item of negotiation in deal-making.
4) Extending (3) further, another option to diplomacy would then be to request a leader to cease trading with a third party, creating an international trade embargo. Civs with which you are in alliance might be obliged to embargo anyone you embargo, but there might also be get-out clauses that can be established, if this would be too punitive for the other guy.