So this is actually several different questions. In order from more to fewer poskim would say "yes":
1) Is it permissible to look at a cell phone that happens to be displaying the time on Shabbos?
2) Is it permissible to pick up your cell phone within your house and move it around for the purpose of having the time displayed elsewhere?
3) Is it permissible to press a button on your cell phone to cause the time to appear?
4) Is it permissible to carry your cell phone (where there's an eruv) and look at the time on it where other people can see you?
The answer to the first question is for sure "yes." Questions 2-3 depend on why you think using electricity on Shabbos is forbidden. Most cell phones today, especially so-called "smartphones," have gyroscope sensors in them and you will be causing circuits to change state merely by jostling them around.
As for question 4, it seems to me that if your cell phone is displaying the time, then it is also on, and so, if a non-Jew calls you, then it will ring, and that would be zilzul shabbos for sure, all other issues aside. Many phones have "airplane mode," which complicates the factors even more.
These kinds of issues are so complicated that only ravs who are also electrical engineers are really qualified to poskin on them, and how many of those are there? Also, each phone would have to be individually certified for "clock use on Shabbos" since the factors are sufficiently complicated that a general ruling would not cut it. In this case, I cannot see how one could justify a "yes" answer to number four under ordinary circumstances.