What modern tools (Windows-based) do you suggest for modeling financial time series?
R is great, but I wouldn't really call it "windows based" :) That's like saying the cmd prompt is windows based. I guess it is technically in a window...
RapidMiner is far easier to use . It's a free, open-source, multi-platform, GUI. Here's a video on time series forecasting:
Also, don't forget to read:
 No, I don't work for them.
I really like to work with R, because in the end you will find almost anything, and you have a very good support with the mailing lists. The downside of R is that helpful bits which fit your specific problems might be spread over a large range of packages, and you might not always be able to find them. Another point may be a lock-in, with that I mean that after a time learning R, you will probably be unmotivated to relearn another software, but this will happen in any system.
With regard to Matlab being expensive - if on a budget, Octave will work just as well, at least it did for the things I needed to do with it, which were rather basic.
I'm new here, and perhaps "financial time series" has a specific definition... But given that I don't know it, my question for you would be what you mean: quarterly/monthly economic data, daily market prices, hourly or higher-frequency data, etc? And by "modeling", do you mean working with textbook ARIMA/ARCH solutions, or things a bit more exotic (such as dynamic linear systems), or exotic/custom experimentation?
R is flexible and free, though less GUI-fied than most. It also has packages covering everything from daily stock prices to dynamic linear systems and optimization packages. (In fact, the hard part will be deciding which time series and which financial packages to use.)
GRETL is free and has a reasonable GUI, though it's econometric, not really daily market oriented. I've heard of Oxmetrics, which appears to have a very complete every-possible-variant-of-ARCH package available for it. If you're talking monthly/quarterly economic data, you could also use X12-ARIMA, which is a benchmark of sorts.
I've used all kinds of GUIs for programming/processing data, but for some reason RapidMiner's never really clicked with me. Something strange about its workflow that I've just never gotten.
While not exactly cheap, MATLAB is widely used in the financial industry for time series modelling: http://www.mathworks.com
At my university, Stata is taught as a programme to do statistical analysis for finance. You can use outreg for example to format tables for publications in financial papers very easily. Programming syntax is not really great I think, you have to declare functions with `variable' for example which is a quirk in my opinion. Amount of different statistical functions however is very vast.
Probably not exactly what you are looking for, but you may check SwiftForecast. It allows you to forecast a time series in an automatic way, without the need of any software. It is quite new, but I find the idea of a "Google style" predictor quite interesting...
You might want to consider using LDT. It is free and while it provides automatic forecasting with stationary vector autoregressive (VAR) models, you can benefit form other types of analysis.
PS: I am the developer of this software.