The examples below set the width to 60 columns. Adjust to your preferences.
NERDTree uses a variable for just this:
This will set the width to 60. You can put this line into your vimrc.
For taglist, you set a similar option:
Like with NERDTree, you can put this line into your vimrc.
Unfortunately there is no generally applicable method. Many plugins do (or should) offer a parameter for this (like above). Others allow you to apply a workaround by setting things you can key off of for an autocommand (such as the filetype, for example, if NERDTree didn't offer the option to set it, you could have done
:au FileTupe nerdtree :vert resize 60, since NERDTree sets the filetype on the buffer). I've found that trying to do an autocmd on the WinEnter event based on the buffer name doesn't generally work when the buffer is created, but does if you leave the window and come back to it; plugins often create the window before setting up the buffer. You'll have to experiment with other plugins or request the plugin author to add a parameter.