A 110W is fine if you have a dual core, no dedicated GPU, one HDD, and don't do anything really intensive on it. For web browsing it would work fine. Though I don't see the point when you can get a Corsair CX400 for like $30.
Edit: Also, those old units are all geared toward delivering +5V power, not the +12V power modern systems need. That means that the wattage is effectively lower. A system like I described would pull maybe 70W during internet browsing, with approximately 50W on the +12V. On an old school 110W that would be approaching the +12V maximum. Also, if it's group regulated then the voltage regulation will probably be a bit wonky, which could cause problems. It isn't a horrible idea to run a system like that on an old 110W, but I definitely do not, do not recommend it.