Am I the only one having issues with this game varying it's speed all the time? Every few seconds the game decides to run slow-mo on me. After a few steps it's back to normal.
There seems to be no correlation with the amount or type of in-game action and the slow-downs,

Running as recommended in [url=http://www.gog.com/en/forum/beyond_good_and_evil/quick_bit_of_info_for_anyone_having_sync_issues]the Beyond Good and Evil thread seems to fix the problem for me.
I though the idea of GOG was to have these issues sorted for us? I find it superbly frustrating that both of my purchases were broken titles, when what I came here for was trouble-free gaming. :/

Had similar problem on my multi core rig, running Process.exe fixed it.(its a bit strange because on my two multi core laptoops it runs just fine without it)
Some older titles have many issues while running on more than one core, it is game-engine depended or something. Sometimes its easy to fix but in PoP case you would have to rewrite a massive part of game core.
I assume that GOG don't have the game source code so all they can do is provide us with some additional software to deal with this issue.

I bought the retail version of PoP and had this problem on an Athlon 64 X2. This issue has since popped up in several games.
Easiest solution is to download the AMD Dual-Core Optimizer; it solves these problems entirely. I'm not sure about an Intel equivalent.

I have a sneaking suspicion that Ubi has a bad PC port team. In fact, now that I think about it I've had performance issues with ever Ubisoft games I've ever played on PC that was a port.

This issue was caused by me having the DirectX SDK installed - thus running on debug DLLs.
After removing the SDK, I have no problems with this game nor with Beyond Good & Evil.
So... both "broken" titles were my fault. Sorry for being a whiny little bitch. :)

I would recommend against useing process.exe since it forces heavy load onto your cpu.
A guaranteed fix for it follows:
1)Start the game normally
2) once the game has started, alt+tab out and open the task manager.
3) Find the Pop.exe process in the process tab (It should be POP.exe unless it was changed)
4) right click the process and click set affinity
5) Uncheck all except core 0 hit ok and exit out of task manager
the game should run smoothly after that. this fix works well on other games that have the same issue

As I said in a previous post, I'm pretty sure the AMD Dual-Core Optimizer solves these problems. Installing it once is a lot easier than alt-tabbing every time you run an app. A quick Google suggests it works for Intel dual-cores as well, as it deals with XP timings and not the actual chips.
http://www.amd.com/us-en/assets/content_type/utilities/DCO_1.1.4.zip

I see that people are having the same problem I am EXCEPT for the fact that I have a single core. its an AMD Turion Mobile 2.4 gHZ and i have extemely slow motion moments with POP sands of time, and good and evil goes out of sync in the cinimatics. Any other thoughts. Its an Alienware with a 256 mb 7900 GS, 2 gigs of ram. tried process.exe and it hasn't helped either game. Any help is appreciated :)

I'm having the same issue on my laptop. I think it's due to the CPU throttling in newer mobile processors (regardless of the number of cores). I'll try playing with my power settings to see if it helps.
In the BG&E forums they mention a problem called gogwrap.exe -- any chance we could also use this for PoP:SoT?
edit: Power settings (including CPU throttling) and CPU affinity have no effect. Turning off vsync helps a little in general but the slowdowns are still there. It's a Core2Duo 2.4 GHz, 4 GB of DDR3 RAM, NVidia 9400M graphics card, and Win7 64-bit RC.

Process.exe made the trick here too.
My specs:
PC - Acer-branded laptop Aspire 6935G
CPU - Core 2 Duo T6400 dual core @ 2.00 GHz (Montevina PM45, FSB800)
GPU - GeForce 9600M GT 1 GB RAM
RAM - 4 GB DDR3 (2 slots)
Audio - Realtek HD Audio (integrated)
OS - Windows Vista Home Premium Service Pack 1
API - DirectX 10.1
Underlining the fact that I haven't bought the game on GOG, here's my experience with Sands of Time: this is the first time I've tried the game on a dual-core system, and just like other users I've experienced random slow-downs while the fps rate is well beyond the playability boundaries....
Tried to change affinity of POP.exe and PrinceofPersia.exe processes, the situation improves a little but not that much. If, after having changed the core affinity, I disable V-Synch with in-game options the slowdowns go almost completely away but then I get no synch between audio and polygons animation during scripted conversations between the Prince and Farah...
Contrariwise, when I use Process.exe (with modified affinity, dunno if it works without too) I can have V-Synch on and no slowdown at all. The game returns to behave exactly like I remembered it on my Pentium 4 with GeForce 4 Ti4200 some years ago.
Oh, and regarding the "stress" Process would put on the CPU: the CPU usage is at 100%, that's true, but after more than 2 hours of non-stop playing EVEREST says me the temp. is still 25 ca. degrees per core, 50� overall. So I can safely say that using Process.exe, even for medium-long term gaming sessions should be perfectly fine.
My two cents, hope it helps someone....
EDIT: Just a footnote: I can confirm that with Process.exe there is no need (at least for me with the aforementioned configuration) to set "core affinity" or whatever to make PoP run as it should with no slowdowns at all (I've checked the last part "10%" of the game, though). The toll doesn't "eat" all the CPU processing power anyway, it just eats one core and leaves the other one untouched. Wonder how it would behave on a quad-core, though.