I have a Nokia smartphone. I just got my wife an Android one (HTC Hero) for Christmas. My mom uses an iPhone, and my dad has one of each. (Yes, he's a gadget geek.)
For what it's worth, here's what I've gathered:
If you want a basic phone, for talking, SMS, and little else, go with Nokia — they're inexpensive and reliable.
If you want a smartphone, it gets more complicated.
Nokia (Symbian): reliable but ugly and boring
Nokia (Symbian) pros: stable, well built, priced attractively, great battery life, very good hardware keyboards on many models, great "phone characteristics" (i.e., voice quality, reception, standards support). (I've used my E71 for a couple of years now, and it has given me absolutely zero problems — it's the first phone I've had in years that has only done what it's supposed to do, with no maintenance, glitching, or other issues whatsoever.)
Nokia (Symbian) cons: dated, ugly-looking user interface, limited apps, dated, ugly industrial design, may need third-party extensions e.g. to sync with Google calendar, fussy configuration utilities, feels sluggish compared to many competitors.
Who would like Nokia (Symbian): businesslike engineer types who just want something that gets the job done ("the job" being phone, calendar, SMS, email, GPS+map, and very, very occasionally checking the web for something), doesn't mind being dropped, doesn't run out of battery easily. Also, who won't care much for multimedia or social network type uses, and isn't bothered by the fact that it looks ugly or dated compared to the competition.
Who would hate Nokia (Symbian): anyone for whom attractive design, a slick UI, or "Web 2.0" style features are highly important.
iPhone: beautiful but fragile
iPhone pros: best and most polished usability and, UI, and design on the market, great app store where you can find an app for just about anything, seamless integration with Mac OS X.
iPhone cons: pricey, poor battery life, technical characteristics (voice quality, reception, ruggedness etc.) at best average.
Who would love an iPhone: Anyone with a Mac who also uses its "iLife" features, anyone who uses the phone primarily for other things than talking on it.
Who'd hate an iPhone: Anyone who primarily uses it as a phone, email, and SMS client; anyone who doesn't regularly plug it into the computer anyway to recharge it; anyone who's afraid of breaking it by dropping it.
Android: just growing into its potential
Android pros: pretty good and rather attractive UI, great integration with Google services, lots of apps.
Android cons: platform still relatively new = frequently updated, quality of handsets varies a lot (the HTC Hero is great, the cheaper ones not so much), battery life is pretty poor compared to Nokia (although better than the iPhone).
Who'd love an Android: anyone who wants both very good basic phone and messaging capabilities and "Web 2.0" capabilities; anyone who already uses many of Google's services; anyone who's willing to take merely good-enough rather than best-of-class performance in most areas.
Who'd hate it: Anyone who hates seeing their handset "obsoleted" by fresh Android releases on a frequent basis (and doesn't want to or can't update the firmware).
I have no experience with Blackberries, nor with Nokia's new Maemo platform (of which I have heard good things, though).
Hope this helped!
