In Civ5, what effects does it have if another civ is "hostile" or "fearful"?

Solution 1:

Fearful

A very noticeable effect is that fearful civilizations will usually agree to unfavorable trade agreements, and even agree to demands via the demand screen ("just give me gold"). Also, you can demand they will not settle cities next to you and they will comply.

Remember, civilizations will not indicate approval to unfavorable trade agreements when you click "what will make this work", but they will approve of the agreement when you click "propose", if they are fearful. They will say something like "well, seems like I have no choice".

Keep in mind that I have had fearful civilizations go directly to "hostile" once they got their military force strengthened.

Hostile

It's very hard to trade with hostile civilizations, you really need to offer agreements that are unfavorable to you for them to agree. In particular, it's very difficult to get open borders from them, even if you offer is otherwise amazingly in their favor. Also, a hostile civilization is - in my experience - very likely to start a war with you if they think they have the upper hand. This can also happen with non-hostile civilizations, but is more pronounced for hostile ones.

Solution 2:

Hostile AI will almost never cooperate with you, or listen. They will be ready to declare war, and may spam you with hate messages. Afraid ai will agree to unfair trades, and demands. However, they usually become guarded or hostile within a few turns.

Solution 3:

Hostile can be a problem: I just played a game where I was trying to get the full set of 15 Luxury Resources (Pearls, Furs, Cotton etc). I started a few wars to take some key cities. Then I found that everyone was hostile to me (something to do with "warmongering"?), and all the resources I had were absolutely useless because noone wanted to buy them off me. That rendered my Bazaars partially useless as well (I was playing as Harun and his special Bazaar improvement can double your resources).