The ArcGIS Server 10 system requirements page says that it supports Red Hat Enterprise Linux (RHEL) AS/ES 4 and RHEL 5. I have RHEL WS 4, RHEL WS 6, and RHEL Desktop 5. I am not sure if any of these version works well with ArcGIS Server 10 without any problem.
2 Answers
Future Proof yourself
ArcGIS 10.1 (including Server)
ArcGIS Server 10.1 will no longer support SUSE Linux Enterprise Server 10 and Red Hat Enterprise Linux AS/ES 4. However, we will support SUSE Linux Enterprise Server 11 and Red Hat Enterprise Linux Server 5.
http://blog.joesonic.com/2011/08/arcgis-101-beta-launch-and-deprecation.html
Offical Source: "Considerations for ArcGIS Server developers: A look toward 10.1"