The answer is
yes. We have used crampons on running shoes. Not real comfortable but if all
you have to do is cross a short section of glacier or up a small snow field
it works.
More often crampons
are used on some sort of heavy hiking boot. This offer more support and can
control a crampon better.
Boots like these
do not usually have a welt that accepts a front and rear bail crampon so a
strap on crampon is necessary. Some boots like the Tecnica Calgary have a
spot for a rear bail but need a strap in front.
A system like
this is generally only suited for walking on fairly gently snow or ice slopes
or across glaciers. These crampons generally have 10 points to the more traditional
12. They also have less aggressive front points which make them weak on technical
ground.
We have 3 crampons
that will work on almost any boot. The G10 comes in 2 forms. The G10 Classic
has traditional straps that must rap around a boot several times in a semi
complex manner (at least the first couple of times).
The G10 New
Classic has a plastic support system and is much simpler to put on and take
off, especially when it is cold. Both of these are on the same page in our
site and are priced the same.
The S12 Articule
is an exception. It is our most versatile crampon. It has 12 points and an
aggressive configuration. This crampon works well on technical mountaineering
routes.
The 2 G10 crampons
above are semi-rigid, they have a metal bar that connects the front and back
but they flex. The S12 is connected with a sort of metal ring that allows
it to move freely. It walks very nice although the 12 point aggressive configuration
takes away from that somewhat. When a fully rigid boot is placed on the crampon
it no longer flexes making it perform well on technical routes in the mountains
(as long as a stiff boot is worn)