Firstly some solutions (some named previously) -
Switch to Gmail: This is your best long term solution. MAC OS X 10.6 Snow Leopard and MAC OS X 10.7 Lion properly supports Gmail/Google Calendar/Google Contacts.
Use mBox Mail: It's been updated to support MAC OS X 10.6 Snow Leopard and comments above says MAC OS X 10.7 Lion too. It was lasted updated in August 2011. This won't sync calendar/contacts just e-mail/e-mail subfolders. It is only a one off fee of $19.99 USD.
Use IzyMail: I believe this works in a similar way to mBox Mail, by way of a web proxy to the companies own IMAP server. This won't sync calendar/contacts just e-mail/e-mail subfolders. The website looks dodgy to me but it is only $18 USD a year.
Use Hotmail.com (or Gmail.com) and forget the idea of using a desktop client. This wouldn't suit me but it does many people.
Use Windows. I know hardly a solution but Outlook 2003-2010 (after you've installed the Hotmail Connector add-on) and the free Windows Live Mail fully support Hotmail's DeltaSync. Which is ultimately what you need to get what you're after.
Even using mBox Mail/IzyMail you still won't have your Calendars and Contacts synchronised. As far as I know, there's no way to get these into MAC OS X software (Hotmail doesn't support CalDAV which is the universal calendar equivalent of IMAP).
All the other options above look very complicated, certainly more so than switching mail accounts (assuming mBox Mail and IzyMail fail).
Migrating from Hotmail to Gmail is much easier than you think. Others have said you can setup Gmail so you can "Send As" your old e-mail address and you can set Gmail to download all Hotmail's e-mail.
This is a pain though (especially if you've got subfolders). If you can get hold of a Windows PC temporarily there is a MUCH easier way. Open Outlook or Windows Live Mail and add Hotmail, also add Gmail using IMAP.
It's then a simple case of dragging and dropping the Inbox and Sent Items contents from one to the other, then dragging each subfolder from one to the other.
This also works when migrating from any IMAP compatible e-mail provider to another IMAP compatible e-mail provider.
Finally Google has equivalent filtering rules, you'll only need to set them up once.
Also see "Comparison with Google Sync" below.
Now to debunk some inaccuracies stated above :-) -
Hotmail supports Exchange ActiveSync for mobiles and DeltaSync for Desktop. It also supports POP3 for mobile or desktop (the only non-propitiatory format it does support).
For all those people who think Exchange support also means Exchange ActiveSync. It doesn't! EAS is an extension of Exchange, it is not Exchange!
It won't work in Outlook for Windows, Outlook for Mac or Apple Mail, all of which support Exchange but do not support EAS. If it used to work by entering the EAS server details into an Exchange compatible client it's more by luck. It's unlikely to be Microsoft stopping you, the technology isn't designed to work that way.
You'd think they could make EAS work on desktops too but literally no desktop client has ever supported EAS (Mac or Windows), there's got to be some reason why that's the case. It could be a technical one or it could be Microsoft doesn't want you using a mobile technology on desktops. We'll never know.
Microsoft are on record as saying IMAP is an old technology and DeltaSync is much better. This is true. It's able to synchronise e-mail, contacts, calendar, tasks and I think notes. It's also much more efficient than IMAP at handling e-mail.
Microsoft's technical reasons for creating a new technology are sound. If you recall it used to be the case that Hotmail didn't support Exchange ActiveSync or POP3. You could only access Hotmail at hotmail.com.
Microsoft aren't going to support IMAP, it's not going to happen.
The trouble is Exchange, Exchange ActiveSync and DeltaSync are propitiatory which require a licence. Apple licensed Exchange and Exchange ActiveSync from Microsoft. There's no reason why Apple couldn't licence DeltaSync (that I know of).
I doubt they will though, to the best of my knowledge only Hotmail uses it and it's clear Apple would prefer you use MobileMe or Gmail. The blame here rests with Apple not Microsoft.
Exchange brings in potential big business support and EAS is the universal mobile standard for e-mail/calendar/contacts sync. DeltaSync just gives Apple Hotmail.
Comparison with Google Sync -
Google Sync supports EAS, POP3, IMAP and CalDAV. Using the latter two methods you can get proper e-mail sync and calendar sync. Outlook or Windows Live Hotmail don't support CalDAV but Apple iCal, Mozilla Thunderbird (with Lightening calendar add-on) and Mozilla Sunbird do.
To my knowledge there's no way to get contact sync except the business Google Apps.
Apple have added their own Google Sync into MAC OS X 10.6 Snow Leopard (I think 10.6 not 10.5) and further enhanced it with MAC OS X 10.8 Lion. They do this using IMAP for Gmail, CalDAV for Google Calendar and I don't know how Google Contacts works but something similar.
Microsoft haven't added zilch Google Sync support to Windows. You can use Mozilla Thunderbird (with Lightening calendar add-on) and Mozilla Sunbird though or if you prefer using Outlook there are plenty of third party Google Sync tools.
I use GSyncit to synchronise Google Calendar/Google Contacts which works brilliantly and obviously Outlook natively supports IMAP.
The best you can expect with Google Sync and Windows Live Mail is Gmail IMAP, no Google Calendar Sync or Google Contacts Sync.