I see you play Games Workshop then
This one should be the most obviously nonsensical and yet still pops up. I wish I had the money to buy sufficient shares to be able to control GW policy and make their success or failure my own private game, but unfortunately I don't. There is no game called Games Workshop, it's a company.
Got your Warhammers in that case then?
Kinda related to the above, where they use the name of the company for a game, here they use the name of a game for the miniatures. They are called miniatures, models, figures, in fact anything you want that makes sense. This question is likely to prompt a response in the vein of "Yes, I have a medieval armoury at home and figured that it'd be fun to lug huge weapons of war around all day."
That's a game for kids
Ok, fair enough, some aspects of it are designed to appeal to kids. Thing is that people often relate it to the toy soldiers they had when they were younger, ignoring the fact that this is an actual game with rules (occasionally far too many of them), tactics and whatever else that elevates it above the level of walking little plastic men around saying "bang, bang, he's dead." A lot of the background is a lot darker than the stuff most young kids will be reading, the rules can get quite complex, and you have to have a grasp of maths and tactics if you want to actually get anywhere with it. These people probably wouldn't walk up to some historical wargamers and say that, but because GW games are easier to get into and have a sci-fi/fantasy (depending which game) aspect it apparently is an entirely different matter.
There you go, three often encountered phrases and why they're wrong. So now that's out the way, what do I actually do myself? Well I used to play 40K (short for Warhammer 40,000) but I'm not too fond of the rules system nor the local people who play it so I mainly just get the occasional nice model for the modelling/painting aspect of it these days. I started on Fantasy (short for Warhammer Fantasy Battles, you can guess why we shorten that =P ) and that's on hold for now, but I do like the system as it encourages proper tactics as long as you avoid certain things/people. Then there's Inquisitor, a larger scale system at 54mm compared to 40K/Fantasy's 28mm though it does seem even larger than that, which is set in the same universe as 40K. This is interesting as GW designed it as a role-play game with a focus on combat and it certainly succeeds at that and some of the models have great conversion potential. The game I currently play is Epic (short for Epic 40,000), which is also set in the 40K universe but is far smaller scale with a human-sized figure being barely a couple of mm high. This allows battles involving huge armies and the rules system certainly favours the use of tactics involving entire formations rather than individual squads (as it should be really). There are also various other games set in both the 40K and Fantasy universes, but these are the ones I've had direct involvement with at some point.
And there we go again with the big posts, and this one didn't even really get anywhere in terms of making a point. Oh well.