Give a look at this post on my blog: http://www.paolocorti.net/2008/06/06/spatial-database-for-postgres-and-arcgis-users-how-to-choose/
Basically you have 2 options:
- use PostGis with ArcSde (so you need an ArcSde license, and ArcEditor if you need to edit data)
- use zigGIS: http://www.obtusesoft.com/ (note that is not tested on ArcGis 10.0). You will just need an ArcView box to connect to it, even for writing data.
Note that if you need Geodatabase support (Domains, topology etc...) or ArcCatalog support, the first solution (with ArcSde) is the only way to go at this time.
As far as I have heard (I did not directly test it) on ArcGis Desktop 10 you can make a read only direct connection to PostGis without the ArcSde gateway.