If I have a page with a form (imagine a simple one with just TextBoxes and a submit button) and I want to allow the user to dynamiccally add more TextBoxes to the form via j
In webforms you won't have a lot of choices if you expect the values to postback and be able to access them in typical fashion. What I would suggest is that you use an Ajax UpdatePanel to allow the controls to be registered at the appropriate point of the page lifecycle (before onLoad), this will also make a difference on whether or not you need the boxes to persist across postbacks. The JS methods involved in the other 2 answers will not persist the textboxes through a postback.
MVC gives you more leeway, since there isn't that crazy page lifecycle, control registration, viewstate, etc to get in your way.
So the big question is, which model/framework for ASP.Net are you using?
Since you are indeed using webforms, I really strongly suggest you go with updatepanels if they'll work for you. it will permit you to add controls in such a way that wont get in the way of eventvalidation, etc.