This app was mentioned in 8 comments, with an average of 2.50 upvotes
Check out OpenGPS Tracker. It's really basic, but gets the job done if you're just interested in monitoring your times and distances.
I like to take photos when I travel, but my camera doesn't have a built-in GPS. I like to be able to geotag my photos to remember where each one was if it's not obvious from the content years down the road. One way around this is to use your phone's GPS via an app and then merge it into the EXIF data using Jeffrey Friedl's Geoencoding Support plugin for Lightroom. The app I use is Open GPS Tracker. It's pretty simple. You can play with some settings like waypoint frequency, but basically you just start it when you want to track and stop it when you're through. It creates a file you can then use in many other applications to create a track map. This is good for things other than geotagging photos, too. If you like to go hiking, you can use it to plot your hike. Same with running.
I use OpenGPS. It's pretty basic, but gives you a map based on Google maps and stats of your speed and elevation over the course of the ride, hike or paddle. You have to manually pause it if you stop, which is annoying, buy I mainly use it for recording my distance travelled rather than MPH.
https://play.google.com/store/apps/details?id=nl.sogeti.android.gpstracker
For what phone? Windows mobile, Android, or Iphone? I personally use Open GPS Tracker
A quick search on the Google Play Store should do the job ;) I found this : https://play.google.com/store/apps/details?id=nl.sogeti.android.gpstracker But it's not the only one :D
Open GPS Tracker. Works great and can be exported to google earth
https://play.google.com/store/apps/details?id=nl.sogeti.android.gpstracker&hl=en
OpenGPS for the actual tracking, then you can upload the GPX file to Strava for record keeping.