I'm sorry I don't know any software but I am curious as to the answer aswell. Plus I feel like educating, if you care
Anyway, I can tell you that there is no such thing as converting to HD. This is because HD is 1920x1080 pixels. most normal videos are 640x480 and below. Pixels cannot be created by magic to try to fill to create better quality. This is where upscaling comes in and is the process you would be looking for in your software. It uses a process called anti-aliasing to improve the apparent straightness of lines in the individual frames. Take a look at these images as a basic example:http://upload.wikimedia.org/wikipedia/commons/a/ae/Anti-aliasing.jpg
It fades some of the black pixels to give the illusion of a more round circle or straighter line.
This is already done during the output process of the video. Using direct x, players like media player classic home cinema (my fav) and VLC (once enabled in the options) will apply the anti-aliasing while you watch the movie.
For what purpose do you need this? Enabling the options will work fine for watching it but if you need to have the actual file converted so that, for example, you can burn a DVD, then you will need the software you are looking for.