Pumpkin

As far as I am aware, and I am not a great pumpkin expert, they will last fine on the vine until the first frosts. I guess, leaving it on the vine as long as possible, will mean that it keeps growing and ripening. I imagine that once picked, however carefully stored, the decaying process begins. Pumpkins can keep for months, but it is difficult to say how long any one pumpkin will keep, that depends on many things. For example, any slight blemishes or scratches on the skin tend to let the rot begin, so a blemished pumpkin will probably not store as long as an unblemished one.
The variety too probably also affects how long it will store. I still have one or two small Hooligan pumpkins from last autumn. The flesh also tends to dry out as they get old. The only thing you can do once harvested is to check on them regularly to be sure you use them before they go off. 

Thank you everyone and especially mum I will leave it until the stem cracks