Private financing and/or ownership of infrastructure hasn't turned out too well in some cases... look at what happened in the UK and some of the disasters in Australia (look up the Airport Link toll road and Sydney's Cross City Tunnel), although in some cases its because of their financing structure. Plus for pure privatization you'd need to give them the power to expropriate, otherwise building a new streetcar line on city streets or building a new highway would be next to impossible without government involvement (I think the rail companies have some expropriation powers right now). I believe the government can also borrow money cheaper than the private sector for large projects. I think in most developed countries the ownership of the infrastructure (i.e. roads and train lines) is with the public sector or a public sector company, even the UK sort of renationalized its rail infrastructure... things like the 407 are leased and regulated, not purely private, although for train lines its different in North America
On the other hand there are also successful examples of PPPs, I think the Canada Line is fairly successful so far and has reduced costs for the government and shifted the construction cost-overrun risk to the private sector, and there are lots of toll bridge PPPs out there. In general it's a good idea to maintain appropriate public control/regulation of infrastructure, avoid unrealistic expectations of the private sector, plan for worst-case scenarios and to not sign any dumb contracts like 99 year leases. In general transportation in all forms will probably always be "subsidized" for many reasons (equity, economic/trade, facilitating interaction etc), however there are definitely ways to reduce the burden on taxpayers/municipalities and improve efficiency by involving the private sector.
Deregulation of local transit operations as proposed by bloor_christie might not be a good idea, based on what happened in the UK (outside of London) local bus system... (as an aside, in that deregulated system the government will fund/tender the non-commercially viable "socially necessary" routes, about 20% of routes/service). I'd like to see some deregulation of intercity bus services or at least a rethinking of the current system (which I think is based on franchises?). Not sure about suburban/commuter rail, but the current model seems to work fairly well and has been making significant improvements, although there is a need for a dependable source of capital funding (tolls, GTA sales tax?).
One possible idea for the GTA would be to move to a Scandinavian model. Metrolinx would take over the planning of all services, create a unified fare system/brand, and would be in charge of tendering routes (not every route would necessarily be tendered, e.g. perhaps they'd want to keep the Yonge subway for themselves/TTC). Maintenance/fleet management could potentially be part of the contract, or could be done separately.
The contracts could be based on the lowest cost for providing transit services (based on guidelines/service requirements in the contract). Metrolinx would keep all fare revenues, although it could potentially use some of the revenue as incentives in the contract to maintain quality service (there would also be penalties for not meeting service standards). Alternatively you can set a price you want to pay and go with the bid that provides the best service for that price (or do a combination of price-quality)
Some routes would be profitable for Metrolinx (i.e. fare revenue generated would be higher than the cost of paying the operator to run the route), others wouldn't. Overall Metrolinx would likely not be profitable, but its costs would be reduced through competition (e.g. In Stockholm this led to a 20% cost reduction while service increased.. it also decreased the subsidy needed for transit, saving the region hundreds of millions).
I don't know that the net cost models that have the private sector collecting the fares and paying for most costs (can have a base subsidy from the government) are always a good idea... there are many instances where the private sector company ends up trying to abandon the route or get a bail-out because revenues are less than expected. Theoretically these models are supposed to shift the risk to the private sector, however in many cases like urbanfan89 noted the government ends up paying in the end.
The TTC would compete with private bus companies for route contracts across the GTA, or it could potentially be sold off.