General:
* Go in
* Come in
* Go into
* Come into
* Proceed
* Advance
* Access
* Penetrate
* Insert
Specific to entering a place:
* Arrive
* Reach
* Visit
* Go
* Come
Specific to entering data:
* Input
* Type
* Insert
* Submit
Specific to entering a state or condition:
* Become
* Turn into
* Transition
* Transform
The best synonym will depend on the specific situation and the intended meaning.