Generally those with valid visas, permanent residency and citizens should not have problems travelling in and out of the US. However, considering the issues we have seen recently, I think it is worthwhile to keep certain things in mind if you are going to travel (and remember, the below is just general information about travelling and is not specific to any case).
First, for those from countries affected by the travel ban. If you are currently a US Citizen or permanent resident you should have no problem travelling. You may face extra scrutiny (by all accounts, they are doing more searches, especially of electronic devices (phones and computers)), but the current orders do not affect your travel. Those on temporary visas are taking a chance by travelling. Even though the travel ban has been suspended, the Court could remove the temporary stoppage order at any time, we just do not know. Alternatively, Trump could issue a new executive order that is more narrowly focused, we just do not know. You just need to weigh the potential risks and benefits of travelling.
For those from countries not affected by the travel ban. Currently, there are no restrictions on your travel. As stated above, there could be extra scrutiny and additional searchers, but whether you have a temporary visa or permanent residence, the current orders do not affect your travel at all.
Remember, the specific facts of your case may also affect your ability to travel so always check with an attorney before travelling to make sure that it will ok for your particular case.