In reply to martinturner
I don't think it's wise to have a general rule but to treat each and every route/outing on it's own merit. To be safe you're probably as well to take two axes if you think there's even a small chance you'll need them, but that's assuming you fully understand the route and/or the conditions you'll encounter - not always the case.
Tools like DMM Fly's have a really good range of usefulness, from walking to technical mixed. I've been using Fly's for 15 years now (the same pair) and they're ideal for mountaineering days.
If you do take a second axe, you might find it easier on some routes to have it attached to a harness (it can be clipped to a caritool or holstered in a gear loop). This works well if there are harder sections or steep snow slopes requiring two axes interspersed with easier walking sections or sections where using one axe and one hand works best. Think something like Ledge Route on Ben Nevis (especially in descent) or the Aonach Eagach. I'll often do harder routes in this way as sometimes you need the second axe while mid-crux so it's convenient to have it easily to hand. If I need the axe to be really easily retrieved I'll holster it rather than clip it - and I'll make sure it's the axe with the adze so that it won't slip through the loop!
A recent example of mine this winter that illustrates how crucial these decisions can be was when I did the Cruachan Horseshoe in early February. I chose to go without crampons and an axe as there was still a lot of powder snow in the mountains. It was a gorgeous, windless day and everything went fine until nearing the Cruachan summit. There's a section of slabby ground here, which turned out to be fairly icy, and with long icy snow slopes immediately below. I had to very carefully pick my way across the slabs, kicking out little toe and finger ledges as I went, something I would have just strode across with crampons on my feet. In my case, I had made a compromise with my footwear that day in order to avoid wearing stiffer boots and crampons (I didn't want to aggravate a foot injury I currently have). But that section, which probably comprises just 1% of the horseshoe, could result in a serious accident as a result of not having the right gear. So even for such a tiny portion of the route it would be worth carrying crampons around for the other 99% of the time.
I guess it's a case of just being aware of what you're packing beforehand (or more crucially not packing) and asking yourself if you're compromising safety? Experience helps but if you have any niggling doubts then err on the side of caution - you'll enjoy your day a lot more.
And as mentioned above, well worth getting a hold of Garry Smith's new book on one axe days in Scotland. It's excellent!