There is always going to be an exception to this rule (legacy apps like Microstation that by design require a mapped drive, etc) but in general you should run them from UNCs based on fully qualified paths.
With a mapped drive you never know for sure where the data is actually located. The intransitive value of X:\ could be anywhere on the planet, and to a user is impossible to identify.
Case Example: User1 is working on their G drive and wants to have User2 take a look at the project but User2's G drive points to a different server. How are they going to resolve this?
Solution: Use a UNC mapping instead (which provides the entire filepath to the user) so User1 could either walk User2 to the location ("Its in \\Server1\marketing\sales\project") or User1 could just copy and paste the path into an email to User2 (who could then click on the link to open that directory/file.
You can access a file on a shared network resource when you type the location of the file in UNC format, or when you browse My Network Places.
To specify a file by using UNC format, use the following syntax:
\\Computer name\Share name\Path\File name
For example, to open a file named Report.xls in the Current\Month folder on a share named Documents, on a computer named Sales, type the following:
\\Sales\Documents\Current\Month\Report.xls
You can also use UNC names to connect to shared resources on NetWare servers. The NetWare syntax, Server/volume:folder, translates to the following UNC name:
\\server\volume\folder:
To open a file by using its UNC name, follow these steps: 1. Click Start, and then click Run. Or, in the currently active program, click Open on the File menu.
2. In the Open box, type the UNC name of the file that you want to open, and then click OK (or Open).
To open a file whose UNC name you do not know, follow these steps: 1. Click Start, and then click My Network Places. Or, in the currently active program, click Open on the File menu, and then click My Network Places in the Look in box.
2. Click Entire Network.
3. Double-click Microsoft Windows Network.
4. Double-click the appropriate domain or workgroup, and then double-click the computer that you want to connect to.
5. Double-click the folder that you want, and then double-click the file.