Characters beyond the 7-bit ASCII range are useful in English as well. Does anyone using your software even need to write the € sign? Or £? How about distinguishing "résumé" from "resume"?You say it's used by scientists around the world, who may have names like "Jörg" or "Guðmundsdóttir". In a scientific setting, it is useful to talk about wavelengths like λ, units like Å, or angles as Θ, even in English.
Some of these characters, like "ö", "£", and "€" may be available in 8-bit encodings like ISO-8859-1 or Windows-1252, so it may seem like you could just use those encodings and be done with it. The problem is that there are characters outside of those ranges that many people use very frequently, and so lots of existing data is encoded in UTF-8. If your software doesn't understand that when importing data, it may interpret the "£" character in UTF-8 as a sequence of 2 Windows-1252 characters, and render it as "£". If this sort of error goes undetected for long enough, you can start to get your data seriously garbled, as multiple passes of misinterpretation alter your data more an more until it becomes unrecoverable.
And it's good to think about these issues early on in the design of your program. Since strings tend to be very low-level concept that are threaded throughout your entire program, with lots of assumptions about how they work implicit in how they are used, it can be very difficult and expensive to add Unicode support to a program later on if you have never even thought about the issue to begin with.
My recommendation is to always use Unicode capable string types and libraries wherever possible, and make sure any tests you have (whether they be unit, integration, regression, or any other sort of tests) that deal with strings try passing some Unicode strings through your system to ensure that they work and come through unscathed.
If you don't handle Unicode, then I would recommend ensuring that all data accepted by the system is 7-bit clean (that is, there are no characters beyond the 7-bit US-ASCII range). This will help avoid problems with incompatibilities between 8-bit legacy encodings like the ISO-8859 family and UTF-8.