For example:
wget http://somesite.com/TheFile.jpeg
downloading: TheFile.tar.gz ...
--09:30:42-- http://somesite.com/TheFile.jpeg
You can use the follow option of tail:
wget somesite.com/TheFile.jpeg --progress=bar:force 2>&1 | tail -f -n +6
The +6 is to delete the first 6 lines. It may be different on your version of wget or your language.
You need to use --progress=bar:force otherwise wget switches to the dot type.
The downside is that the refreshing is less frequent than with wget (looks like every 2 seconds). The --sleep-interval option of tail seems to be meant just for that, but it didn't change anything for me.