Do these EScs have governor mode?   

Nope - even though the ads say they do.  They do have a prop brake, and are sport-flyable if you use a timer that constantly advances the throttle setting like Wil Hubin's FM-0c.  (I believe some other timers also work that way but I do not have direct experience with them)

I have a Turnigy 35A in an OTS bird and it works OK but it will never be mistaken for a Phoenix!

Castle Phoenix is probably the most economical - Since the ICE came out, the Phoenix can be had for a little less than before.  There is also the Jeti (don't know which models have all the features - pretty sure the Jeti Spin does) and you may be able to still find an Atlas, which I think Wil Hubin said works pretty well.  The Hackers are (or used to be) re-labelled Jeti's.  None are 'inexpensive' compared to the Chinese ones, but really not that bad.

I really must stress that Governor mode is not absolutely necessary - I've been flying a Twister on a 3-cell setup with a Super Simple 50 amp ESC and a Hubin timer (with the throttle 'advance' feature).  I have done more complete patterns in the past year than in the previous 10 years combined (all glow powered).  I have also used a JMP-2 timer, which also has the advance feature, as does the Z-tron (don't know which model).  If you can somehow account for the battery droop, you can get a system that will fly through the pattern.  I use 4200 mah (3s2p) and 3700 mah (3s1p) batteries and set the timer for 5:20.  Power through the 4-leaf is more than adequate.  When Spring gets here, I will be starting to get a 4-cell setup going and have a Phoenix 45 for it, but a minimal amount of testing done late last fall showed that while it is noticeably better than the old setup through manuevers, it isn't absolutely necessary.

A smaller (30 amp) system, flown mostly for sport, is also flying well - though un-governed.  This is the one that I have tried 3 different Chinese ESC's - supposedly with governor - on, including one of the Turnigy's (Plush, I believe).  Like I said above, none of them actually governed nor had any method of setting a governed RPM.  One of them - supposedly a 'heli' model - would only run the motor at about 2000 RPM in Governor mode, though it worked normally with Governor mode turned off.  The Plush and one other didn't appear to have any effect whatsoever with Governor mode turned on, versus with it off.

Thanks Mike and everyone. I did some more web surfing and found that HobbyKing sells a Turnigy ESC series:
PRODUCT ID: TSB20A
Turnigy Super Brain 20A Brushless ESC
link
http://www.hobbycity.com/hobbycity/store/uh_viewItem.asp?idProduct=10940

Programmable settings;
Startup (Default Standard/Soft/hard)
Low Voltage cutoff (Default 5.0/6.0/7.2/8.4/9.0/12.0V)
Current limiting (Default Standard/Very sensitive/Insensitivity/Disabled)
Brake (Default None/Soft/Hard)
PWM rate (8/12/16 KHz)
Timing (Default Auto/Low/Middle/High)
Cutoff type (Default Hard/Soft)
Governor mode (Default Auto/Low/High)

At $29 for a 20A version it is moderately priced. The main feature is that it has a data logger with USB link just like the CC ICE. Seeing as how I am a low budget flyer I will probably try it.

More of their blurb:
Features:
Supports the ‘Turnigy USB Linker’ to program the ESC by computer.
Internet upgradeable ESC firmware.
Integrated flight data logger, records data for the ENTIRE flight such as:
- Voltage
- Current
- Temperature
- Motor RPM
- Throttle travel

I line item I marked in red is not a governor - rather it is a "throttle curve". My understanding is that it is used by the Heli-boys to bias the throttle response from linear to achieve a nonlinear response which (I guess) makes it easier to fly your Heli.

The data logger is an interesting add-on.  Will Hubin has a timer model where you can actually adjust how fast the throttle advances. Thus you could, over a series of flights, watch the RPM read-outs and adjust the timer's throttle-up settings to get as close to constant RPM (beginning to end of flight) as possible...

Just out of curiosity, if you are using throttle, why do you need Governor mode?  Governor mode can only operate if you are flying at less than full throttle.

Hi Mike,
The RPM governor  mode is by far better for flying Stunt than any fixed throttle setting.
The governor will actually add power in the uphills and reduce it in the dives, not to mention keeping the lap times consistent throughout the flight as the battery voltage droops. In order to do this, the "throttle" that is internal to the RPM control loop must never hit full throttle, but instead needs some voltage headroom to do its thing. As a general rule, I suggest that the running RPM be set to somewhere around 75% of the multiplied product of the normal loaded battery voltage (3.6 V/LiPo cell) and the Kv of the motor in RPM per volts.

I addition, we have found that some ESC governors are slow to respond. The ones with the good fast response times to sudden load changes (like a square corner to a climb) will actually hit the motor with an extra pulse of current in under two-tenths of a second, which dramatically improves the lock coming out of the corner. Also, tighter RPM  control prevents wind-up in runway wind conditions much better. The Castle and Schultze ESCs seem to be head and shoulders better than the rest, but I'll let other tell of their experiences.

Hope that helps,
Dean Pappas