How can I convert a 1080p wmv video to a 720p video?

Since you used an ffmpeg tag I will use that for the answer.

ffmpeg -i input.wmv -s hd720 -c:v libx264 -crf 23 -c:a aac -strict -2 output.mp4

Change the video quality by specifying a different CRF parameter. See the x264 encoding guide for more info.

Time has moved on a little since the original accepted answer for this question in 2012. Newer versions of FFmpeg would be better to use FFmpeg's 'scale' video filter.

I give an example below, using this filter, which also simply copies the audio track as you have requested:

ffmpeg -i input.wmv \
       -c:v libx264 -preset veryslow -tune film -crf 22 -vf scale=-2:720 \
       -c:a copy \
       output.mp4

The -tune film option given above can be omitted or you could try -tune animation depending on the type of video clip you are using.

If you decided that you would like to transcode the audio a good choice would be to use the external library libfdk_aac as follows:

ffmpeg -i input.wmv \
       -c:v libx264 -preset veryslow -tune film -crf 22 -vf scale=-2:720 \
       -c:a libfdk_aac -b:a 128k \
       output.mp4

This is certainly what I would do with a wmv file that I was scaling, you will find the results more than acceptable...

If you want to keep intact all the audio tracks, subtitles and so on, you should use something like this:

ffmpeg -i input.mkv \
       -map 0:0 -map 0:1 -map 0:2 -map 0:3 -map 0:4 \
       -vf scale=-1:720 -c:v libx264 -crf 18 -preset veryslow \
       -c:a:0 copy -c:a:1 copy -c:s copy \
       output.mkv

In this case, the input.mkv file has two audio tracks and two subtitles. You can specify all the audio tracks (or subtitles, or videos, etc.) one by one or as a single entity (as I specified for subtitles).

Hope it helps...