There are a few ways...
As Robbiedeluxe mentioned, you can use your phone's browser and go to places like mobile.google.com and type "UA 835"... this will give you a flight status. Or you could go to a carrier's own mobile version.
If you want to see avail connections from different airlines at once, I believe that getting a software like
Mobimate WorldMate could be the best choice.
Lastly, if your phone is limited, you could always send a text message to GOOGLE (466453) with a string like UA 836. You will get a text message back within a few seconds.