Which are the excluded taxes, discounts and advantages to have a hybrid car in US?

If I understand correctly, I would say no - you are not allowed to drive on the median or shoulders because the car is a hybrid - no vehicles are allowed to do this. You are only allowed to stop on the shoulder or median in an emergency and you should move as soon as possible.

You are allowed to use HOV (high occupancy vehicle) lanes aka carpool lanes in California if you have a special decal which were issued to qualifying hybrids that have FE rating of 45 mpg or higher. This program will be ended Jan 2011 unless it is renewed by the California legislature (not likely).

There was a Federal Tax Credit allowed for certain hybrid models. The original tax credit was $3000 USD until Toyota sold 60,000 units, then the credit was phased out over the next year. I received $1575 tax credit for buying my Prius in Feb 2007.

New Energy Tax Credit for Hybrids

In California, besides the use of HOV lanes explained above, some cities allow free parking for hybrids which have the Clean Air decal.

LA City Council Approves Free Parking For Hybrids - cbs2.com

In California, most vehicles must be tested for emissions every 2 years (biannual testing). The test costs between $30 - $60 + $8.25 for the smog certificate (even though it is electronically transmitted - there is no actual certificate for the $8.25 ). Certain hybrids including the Prius are exempt from smog testing until at least Jan 2010.

Hybrid-Electric Vehicles Exempted From Initial Smog Check

 

To the OP: With the exception of the Federal tax credit, described above, most benefits for a hybrid come from state laws or even local ordinances, so it will be hard to say anything US-wide. (Unfortunately, as described, the tax credit's long gone for the Prius.)

I'd add: in some areas, the HOV lanes are shoulders during non-peak hours. So that may be what the OP's friend was describing. (Around here, the left lane becomes the HOV lane, and the right shoulder becomes an extra lane.)

To clarify: HOV lanes are restricted to vehicles containing 2 or 3 (HOV-2, HOV-3), or perhaps more passengers during certain hours.

Here in Virginia, if we get Clean Fuel license plates (only certain vehicles, like the Prius are eligible), we can drive in most HOV lanes with only a single occupant. We are also exempt (seemingly for the life of the car, but maybe I'm wrong on that) from emissions inspections.

I paid extra for the Clean Fuel plates because we live inside the Beltway, and during rush hour, the nearby interstate I-66 is unique in that ALL lanes are HOV. I don't particularly want to get into an HOV lane, I just want to be able to get onto that road.

In Baltimore, Maryland, there are some city-owned parking lots that give free parking for hybrids, and I've seen a couple of "reserved for hybrid" parking spaces at the local mall (private property, not government-owned).

 

I can't vouch for the accuracy of Hybrid and Plug-in Incentives and Rebates - Region by Region | Hybrid Cars, but I know one item there is wrong, for Washington state. It ended early on Aug 1st 09 per http://dor.wa.gov/content/aboutus/newsroom/html/051909.aspx.

I used to live in California and I can say there was basically no state incentive other that the HOV (carpool) lane stickers, which are useless outside CA. I did get the $3150 Federal tax credit since I bought mine WAY before Toyota hit 60K qualifying hybrids sold starting from Jan 1, 2006.

 

Something I learned here on Prius Chat. In New York you can get a "Green Easy Pass" which replaces your regular one. You get a 50 percent discount on Port Authority bridges & tunnels ($4 instead of $8) and a 10 percent discount on the NYS Thruway. Regular discounts on other tolls. Note: Apply for the pass through Port Authority and you pay no monthy fee, Apply through NYC Bridge & Tunnels and a monthly $1 fee is charged. Contact the Easy Pass office and they will send you the applications or visit one of their customer service centers which is what I did.

 

London's Congestion Charge zone is an area about 8km by 5km covering Nottingh Hill, Kensington, Chelsea, Hyde Park, Marylebone, Soho, Westminster, Lambeth, Finsbury, the City of London, and Southwark. (There's an exemption for one north-south road that passes through the middle of it.) The charge is £8 to enter if you pay in advance or on the day, or £10 if you pay the day after. (After that it gets very expensive.) There are bulk discounts for regular users.

Residents of the zone automatically get a 90% discount, but still have to pay it. Anyone, resident or not, with an Alternative Fuel car that has less than 40% of the limits for NOx and hydrocarbon emissions for Euro IV can register for a 100% discount for an annual fee of £10. NOx and HC are the prime contributors to smog formation.

Those rules cover a lot of flex-fuel LPG cars as well as hybrids, even though most flex-fuel vehicles are always fuelled and driven with petrol. There's a list at PowerShift Register / Publications / Global Data / UK Home - Energy Saving Trust. The first vehicle on the list is a Jeep Grand Cherokee 4.7L V8 LPG conversion!

There's a proposed change to the rules so that any car emitting less than 100g/km CO2 on the EU emissions test and meeting Euro 5 will get a 100% discount. Any older cars not meeting these demands will no longer get a discount after the rule-change. The second-generation Prius emits 104g/km CO2, so will be excluded, even though it beats Euro 5 by miles. (NOx emissions are 0.01g/km, limit is 0.06; HC emissions are 0.02g/km, limit is 0.1.)

I'm not aware of any other exemptions. There are no incentives to buy a hybrid any more, which there were at one stage.