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Thanks to those above who suggested this fix. It was very useful, but I think there is an even easier to correct this. You don't need to remove the Exchange account. Here is what I did to fix this.
1) Removed data from Calendar, Calendar Storage, Calendar Sync Adapted and Calendar Widget (basically anything with Calendar in) using Manage Applications under Settings/Applications.
2) Opened Settings/Accounts & Sync/Exchange Active Sync and unticked Calendar sync.
3) Did a "Sync now" which therefore just sync'd mail and contacts.
4) Ticked "Sync Calendar"
5) Did a "Sync now" which sync'd mail, contacts and calendar.
Problem had gone away. I actually believe this is a problem with the Exchange Activesync profile as something pretty similar used to happen on my Nokia (which uses Activesync, as does iPhone) and I used a similar method to fix this but I can't be sure of this.

I've had a Desire for two weeks now. I was in love with the phone... until this problem came up.
I use Outlook and Microsoft Exchange -- and had read all about how Android synced easily. And it did at first. Then, 10 days ago, the calendar stopped syncing. I got a "Client/Server conversion error," and no sync. The problem only effected my calendar -- mail and contacts were synced just fine. After reading a few forums, I did a "Remove account," re-installed the account. It worked fine again. No big deal.
Then it happened again today. I did the Remove/re-install thing again, and again it was cured. Until six hours later.
Is anyone else having this problem with their calendar/exchange sync? Any solution guesses?
Help! Without being able to sync my phone to Outlook, the Desire I love so much is somewhere between frustrating and infuriating.
Thanks in advance,
Jon
I've had a Desire for two weeks now. I was in love with the phone... until this problem came up.
I use Outlook and Microsoft Exchange -- and had read all about how Android synced easily. And it did at first. Then, 10 days ago, the calendar stopped syncing. I got a "Client/Server conversion error," and no sync. The problem only effected my calendar -- mail and contacts were synced just fine. After reading a few forums, I did a "Remove account," re-installed the account. It worked fine again. No big deal.
Then it happened again today. I did the Remove/re-install thing again, and again it was cured. Until six hours later.
Is anyone else having this problem with their calendar/exchange sync? Any solution guesses?
Help! Without being able to sync my phone to Outlook, the Desire I love so much is somewhere between frustrating and infuriating.
Thanks in advance,
Jon

This is what worked for me
1. Menu > Settings > Accounts & Sync > Exchange ActiveSync
- Uncheck 'Sync calendar'
2. Sync the Account
3. Menu > Settings > Applications > Manage > All
- 'Calendar' : Force Stop, Clear Data, Clear Cache (if avail)
- 'Calendar Storage' : Force Stop, Clear Data, Clear Cache (if avail)
- 'Calendar Sync Adapter' : Force Stop, Clear Data, Clear Cache (if avail)
3. Sync the account again, get there just like in step 1.
4. Verify the calendar is empty.
5. Menu > Settings > Accounts & Sync > Exchange ActiveSync
- Check 'Sync calendar'
6. Sync the account.
I'm having similar issues with an HTC Merge, both contacts and calendar were not syncing, except I got the error: "error occurred on the computer running the exchange server."
I tried the suggestion above and that got the calendar running again, but contacts still won't work. Any suggestions?