Abraham was God's friend because God chose to consider him his friend. It's the only such case mentioned in the Bible. It wasn't Abraham's choice, it was God's.
It's unknown to me as a Christian if God wants to be my personal friend or if I should pursuit a friendship with God. Certainly Jesus didn't teach us to be friends with God; nevertheless he said he considers his disciples as his friends, although in a conditional sense (=if we comply with his commandments). It is what it is; Jesus and God are on an entirely different league, and they own the game. We're not supposed to be 'buddies' type of friends. Why should we whine about it?
As pointed by Searcher, we are God's children, and brethren with Jesus. That's what we should look forward to. There's an immense measure of respect and love involved in a relationship with a father, much more with the heavenly Father. We're not buddies with God. We can be His children, based on the faith we put in Jesus, and when our heavenly reward is awarded, then we can expect perhaps a greater closeness with God, which will come along with greater knwledge of God on our part. Interestingly, the apostle Paul said that it's God's will that 'everyone should be saved AND come to an exact knowledge of the truth' (1 Timothy 2:4) The full knowledge of the truth comes after salvation, not before salvation. To fully understand God and Christ isn't a pre-requisite for salvation as sometimes the JW's make people believe so to persuade them to accept a Bible study with them. Yes, some knowledge about God and Christ is necessary in order to build up faith (John 17:3), but not full knowledge. That will only be attained - hopefully - when each one of God's children inherits the Kingdom.
But until then, the relationship we can establish with God is that of a "child of God".
Eden