I want to have a text field in a C# winform application, and the effect I want is that as the user types stuff in the text field, the program searches a database in the background, and then generates a drop down list for the user to choose from ..
Here are two web based examples but do note that my application is winforms based, not web-based .. I just want the same effect, which is why I’m showing these:
cinemasquid.com:

blu-ray.com:

How can I get the same effect for a text field in a C# winform application ?
If you don’t want to code your solution there are a handful of custom controls avaliable via Google search, for example: http://www.dotnetfunda.com/articles/article225.aspx
BUT you should keep response times in mind: if you code a database search everytime the user enters a letter on your textbox, your application could get sluggish and/or unresponsive, depending on number of records on the table, speed of your network connection and a lot of other factors.
Consider preloading a collection of strings (name, titles, whatever it is you want to display on the textbox) on memory and then performing LINQ queries to that in-memory collection to populate the autocomplete part of your control.