Declarations of Friendship are useful, if the conditions are right. I was recently in a scenario where on a 5 civ continent, I was smack in the middle, along a narrow stretch, effectively dividing the continent in 2 with my empire. I had three potential enemies - Arabia to my north, and Gandhi and England to my south.
Recognizing Gandhi as a friendly, non-warmongering guy, I pursued friendship with him. I also befriended Russia, who was the 5th civ on the continent flanking Arabia. I signed Defensive Pacts with Gandhi all game to protect us against England (who we eventually outteched and warred). I signed a Defensive Pact with Russia to protect myself against Arabia. With that, I avoided a DoW until turn 240 (Russia had run through Arabia and made it to me). Ironically I held them off in part to selling a border city to Mongolia, which slowed down Russia's army for some turns until they warred through it. I lasted just long enough against the onslaught to win by space race.
So, Declarations of Friendship are helpful when you and another civilization have a common enemy. You just have to remember which leader they are (look up their deception rating), what the benefit is for you, etc. to evaluated whether or not it's worth it.
Just FYI, my strategy for DoF's is as above, plus I sign them with allies of my friends and with civilizations with corner starts (who have the fewest enemies). I don't get asked for things until very late game because I sell all surplus luxuries and don't keep a large sum of gold on hand.
