So far I've never actually tracked how far and how fast I'm going, but I've been curious about this.

Does anyone have any recommendations for a good way to do this using an android phone?

I figure if I'm going to do this I'd rather use what I already have on me than carry any more gear.

I use Ulysse Speedometer Pro. Very feature packed, can import tracks to Google maps, UI is quite customizable, etc. Battery usage isn't all that bad and I often just put my phone into airplane mode w/ gps turned on.... it lasts hours and hours.

I will often keep it in a waterproof case on my gooseneck to offer a large, highly visible speedometer display that is much more easy to read while at speed than most all handheld GPS units. Which is what I really like about it.

Obviously not as accurate as a dedicated gps, but I'm not looking to set/record speed records either. It does what I think you're looking for quite well. Also available in a free version.

Oooh, that definitely looks like what I'm looking for. Don't even need a waterproof case as my phone is waterproof already.

Now all I need is something comparable for my smart watch in the mail so I don't even need to keep my phone visible.

I've used mytracks happily for some time.