I think it's most important to get really familiar with the sound of good music on whatever devices you do the bulk of your mixing work. Make sure to know, or find out, what sonic weaknesses each one has, and use other devices to fill in the gaps to check your mix and fix those areas. If the end product will be used in a specific listening environment, it might be a good idea to check your mixes in an environment as close to that as you can reasonably replicate.
If you mix mostly on headphones, check out Inner Fidelity's headphone measurements to see a graph of the frequency response for the make/model of headphones you have -- this will help identify potential problem areas.
There are also plugins out there designed to cancel the frequency response curve of various models of headphones, so that what you end up hearing is completely flat. (Once you have the frequency response graph, you can try doing this manually with an EQ as well.) I haven't tried any of these solutions, but some people swear by them. My biggest issue with this type of system is that music you listen to normally (without the plugin) would sound different, and so you wouldn't really "learn your headphones." There are advantages and disadvantages.
I think learning a good pair of headphones is mandatory. Headphones remove almost all the variables associated with the (usually poor) sonic characteristics of the room in which you're working, and also gives you a consistent sound no matter where you are. What if you like to travel and have to do work on the road? What if you move to a different house/apartment? It's basically impossible to take the sound of a room along with you.
For checking mixes on small speakers, I've found that a good substitute is to put a high-pass filter on the master fader at around 115 Hz (add this to your mixing template so it's right there to be turned on/off when needed), and then listen to make sure elements such as the kick drum and bass can still be heard from only their mid and high frequency content.