Depends on why you’re being dependent.
If you feel like you’re being too dependent because you need to run everything you do by someone else to get their opinion or find out how it affects them, then you’re having problems with owning your feelings. Doing things “for” someone else constantly makes them responsible for whether it’s good or bad, and removes the onus from you. Try pretending you’re the other person whose opinion you’re soliciting – imagine what you would say to someone else who came up to you asking what they should do. People like this tend to be much harder on themselves than they are on others. You might find it enlightening.
If you find yourself wanting to run to someone else when things get tough to the exclusion of everyone else, there are a few things you can try. If you’re doing it because you want comfort over something external (i.e., events that don’t concern the person you’re running to), then you can create a model of this other person in your head. Ask yourself, “What would he do/say if he were here?” This isn’t ideal as a long-term solution, as it’s still allowing you to get by without learning how to soothe yourself, but as a stopgap measure it may be what you need to get through until you have the time and space to work on yourself further.
If you keep running to this other person to hear that they love you and won’t leave you in lieu of discussing or getting comfort over the external bad things, then what you need to do is develop what’s called object constancy. At its root, object constancy is the belief that things remain the same whether you’re looking at them or not. Toddlers develop this about the concrete world when they work out that a ball rolling behind an obstacle isn’t gone, but will eventually roll out the other side. When it refers to people, it means coaching yourself to believe that your relationship will not suddenly mutate into something completely different just because you’re not together and can’t ask him about it all the time. There’s nothing much you can do about this other than recall what he said and did the last time you were together, and how it made you feel, and tell yourself very firmly that you are GOING to believe this state of being remains true UNLESS you get explicit notice that things have changed.
Finally, if you feel like you’re being too dependent specifically because you keep running to the same person and are afraid it’s too big a burden for them to bear, then you can consciously select someone else trustworthy to lean on, and force yourself to sit down and tell them everything. It doesn’t necessarily have to be a friend or family member – if you would prefer to tell someone who is in no way involved in anything that’s happening right now, you can get a therapist, call a counseling helpline or visit a chatroom, or if you’re religious you can ask to talk to your local rabbi/clergyman/high voodoo priest/whatever. This is particularly helpful if you judge how badly off you are largely by how much other people wince when you talk to them.
I wish everyone who’s struggling with this the best of luck dealing with it. I’ve been working on similar issues for most of my life, and I still sit in the corner and have vicious arguments with myself over it sometimes. It’s not fun and it certainly doesn’t help when you feel like not only are things going wrong, but you’re dealing with it wrong somehow, and you don’t know any other way.