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 PostGisPostGIS with ArcSdeArcSDE (so you need an ArcSdeArcSDE 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 Geodatabasegeodatabase support (Domainsdomains, topology etc...) or ArcCatalog support, the first solution (with ArcSdeArcSDE) is the only way to go at this time.
As far as I have heard (I did not directly test it) on ArcGisArcGIS Desktop 10 you can make a read only direct connection to PostGisPostGIS without the ArcSdeArcSDE gateway.
zigGIS is no longer active and the website is offline