Try doing activities with your friends. For example gym, lunch, cinema, comedy's etc. Helps the bonding process. I know my friends are there if I need to talk to them, yours should be to, but as you said you can't over abuse it or they get fed up. If you want closer friends if you don't have them then get out there and meet new people in classes/sports etc.
Here is a story about my own life:
I recently met an old friend i used to work with pushing trollies at a supermarket, we spent 9 hours a week together every Saturday for a year. We bonded well and i was sad when he left, wasn't quite the same without him. He left to live in costa rica for 6 months. This was three years ago.
By chance we met at a restaurant where my ex and myself were. He got in contact with me over MSN. We arranged to meet up and have since become good friends. With this 3 year gap we had the chance to mature in to new people (he wasn't as outgoing as he is now). We recently went on holiday together to prague - a real chance for bonding and me and him now regually attend Badminton and gym together as well as sharing lifts to work and pubbing!
Thats just a message to everyone, that who knows what the future holds, this could include ex's as well. A chance for growth and then meeting again

The future is bright