I like the idea of promoting mathematics to students, i.e. more explanation of the contribution of mathematics to civilization, so that students have some language and background to justify their subject. See my web page www.bangor.ac.uk/r.brown/publar.html
On specific subjects, I have enjoyed showing first year UK students the power of the symbolic algebra packages on dealing with Grobner bases, i.e. solving polynomial equations in more than one variable. To more advanced students one can give exercises like:
Find a polynomial in x,y which has more than 5 critical points, classify them as max, min, saddle, and use the computer algebra package to draw your function and display or indicate the critical points. Verify with the package that the points you find are critical points.
(The last part gives useful lessons in rounding accuracy.) The whole exercise gives students a nice sense of power, as the machine manipulates vast expressions!