TheFifthHorseman

Is there a common situation when the crashes occur - like opening the contacts list, zoning, or using a specific power - or do the crashes happen out of nowhere? Is COH the only game or program you're experiencing crashes with?

If anything, I can only add to the possible points of failure.
Your description of the symptoms comes fairly close to what I've encountered when my power supply started failing, down to the fact that reducing the power consumption a little (by removing the RAM module) made the difference between not booting at all and booting more often than not. When the rest of the system is not getting enough power to work under peak load, unstable behavior is fairly normal.
The way to confirm that is monitoring the voltages output by the PSU and comparing them to the ranges they were supposed to be in.

Uninstalling 9.3 completely and installing 10.2 has - seemingly - caused the crashes to worsen. After installing 10.2, the crash happened immediately when talking to a contact or trying to check another player's info. I've also tested and confirmed that the crashes also occur when starting the game in safe mode.

I am now certain that this is another incarnation of the previously reported "crash on portrait display" bug - since that is the common denominator in all cases (contacts tab, player info, talking to contacts, opening my own costume selection window).

From a more practical standpoint, allowing the players to see the various Paragon Reward pieces would be an incentive for the players to subscribe / buy points to progress further in the rewards program.

O.o *That* is considered a swear-word here? Fine, make that: barbarian horde (whether or not it comes from Asia).

It appears that free users aren't only limited to posting in Gameplay/Technical Issues & Bugs, but in addition cannot reply to threads started by anyone other than themselves (Yes, I am logged in; No, the threads are not locked; According to the permissions reference at the bottom, "You may post replies").

I don't know whether or not that's intentional, but it does get a tad annoying to see someone reporting an issue I've experienced myself and be unable to provide him with any of the information and advice I have on the subject.
I entirely understand the reasoning behind restricting us from posting in any forum other than this one and agree with the notion; this additional restriction, though, makes no sense to me.

Free players are not some kind of ****** horde that will charge through the forum spamming every thread in sight. Sometimes we too can provide information or answer someone else's question.

Correction, crashes still happen - but they're a much rarer occurrence now.

The water effects were disabled the entire time.

It seems I managed to solve the problem by changing my GPU settings. In the Catalyst Control Center, I've disabled Adaptive Anti-Aliasing, Catalyst AI and VPU Recover, then in the game I've disabled anisotropic filtering and decreased character model detail to 80 %.

After that, I've been able to run the game for six straight hours, multiple plot missions and multiple interactions with different contacts without a single crash.

I'm not exactly sure which of the things I did made the difference, TBH. Most likely culprit is VPU Recover - I've seen quite a few mentions of it causing crashes in games.

There seem to be two past incidents where similar issues were described:
http://boards.cityofheroes.com/showthread.php?t=193115
http://boards.cityofheroes.com/showthread.php?t=248462

Some further googling indicates I need to either change my graphic settings or uninstall the official ATI drivers and install a modified version called "Omega drivers".

The downgrade fixed something, since display glitches in Blender (which kept plaguing me when I installed 10.2) are gone, but no change with CoH.
The crashes occurred twice since and true to established pattern: when logging in again after that crash (with the Nav/Contacts dialog open) - and then when talking to a character to complete a mission.

Three more: Talking to a character during a mission (when it was supposed to trigger several mobs to spawn), passed just fine the next day. Opening the Contacts tab in Nav and logging in after the reboot from the last one.

That last one happened after I manually shut down just about every non-essential software running in the background, so we can be reasonably sure it's not that.
After checking the ATI drivers page again I've noticed that the version they announced would be the last to support the Radeon 9600 series (9.3) is older than the one they directed me to download last time around (10.2). I'm going to try downgrading to 9.3 and see if it changes anything.

Three further freezes: first when switching to the "Detectives" tab in navigation, next was immediately upon re-entering the game after rebooting from the last one, the last occurring when I brought up the costume change menu (which worked fine literally a minute earlier).

The last freeze was connected with two symptoms: first, I tried to bring up the costume change menu using the K button. For some reason, that failed to occur, so I clicked the menu and tried to start it from there. That made the costume change menu show up - with my primary and secondary slots both showing the "unlock slot this in the game" message - upon which it froze.

Unless I'm missing something, each time seems to be occurring when my copy of the game is trying to communicate with the server (I'm playing on Union, BTW).

Nevermind, got past that one too.

After finally getting CoH onto this machine (and all the required updates to my system beforehand), I've started the game today with a Tech Blaster Hero.
I've encountered an apparently consistent crash in the "Save Matthew Habashy and Atlas from Arachnos" mission given out by the contact Aaron Thiery. At the end of the Arachnos base instant, I'm supposed to talk to Matthew. When I do that, the game freezes my system completely - I can't alt+tab back, call up Task Manager or do anything other than a hard reboot of my system.
I'm not sure if it's related to the problem, but Matthew remains face-down the entire time after I've defeated the enemy guarding him.

Output from COHHelper (mind you, it's still giving me an error about the COH registry data not being found):

There have been multiple logs saved in the NCSoft Launcher's program directory. Since all of them are massive walls of text, I've put copies of the log contents on Pastebin if they're needed for reference:
http://pastebin.com/pcikeiDd
http://pastebin.com/aCxb8vai
http://pastebin.com/yPL5qWch
http://pastebin.com/ddurSdLh
http://pastebin.com/7FLBEmnX
http://pastebin.com/3XLK2S2W
http://pastebin.com/xPbNjufr
http://pastebin.com/LYvSLFUp
http://pastebin.com/w2XJxNT1
http://pastebin.com/ChrkZpn5
http://pastebin.com/i7g56q6E

HijackThis log follows:

I've downloaded the NCSoft Launcher and started the installation yesterday. Throughout the process there was a number of times when the launcher just flat out crashed, some of which involved a message about attempting to access protected memory (note: I'm reasonably sure my desktop's RAM is fine; both modules have been installed two months ago and everything I run here has been stable except for the Launcher).
Eventually, it completed downloading the first stage of installation and I went on to character creation. Once done (about 1 and 1/2 hours from the start), I've found three things: first, I could not save my newly created character; second, Stage 2 did not download at all and was at 0% progress; third, after tabbing back to Windows I found that the Launcher has displayed a window with the message "The operation has timed out". I've attempted restarting the Launcher entirely, but the issue continues to occur. Effectively, I am unable to do anything but mess with the character designer.

Running the "City of Heroes Helper" as described in the sticky thread gives me the following error message before the program finishes: