Wow, I could have written your request! My 16 MO daughter walks pretty well as long as she's got a piece of furniture, a walk-behind toy, or just one of our fingers, but as soon as we let go, it's maybe 2-4 steps. I think with her, it's a confidence issue. As soon as she realizes what she's doing (even though she seems to enjoy walking), she freezes and plops/falls down. The older girls at her daycare have started encouraging her a lot (it's a fun game for them), and I think that's helping. Otherwise, by the time she gets home in the evening to practice with me and daddy, she's too tired. We were more worried because she was walking in a severely pronated angle on her feet (on the inside edges of her feet, which is impossible to balance on!), but that seems to be getting better as her feet become stronger, and her ped. wasn't worried.
I'm really not too worried about mine ~ she obviously wants to walk, so it'll come one of these days. I think one day she'll have just the right motivation and she'll take off. She's also starting to climb on everything, so I'm already wondering why I'm in such a hurry to have to chase her more! :-)