Information
TableTop games covers pretty much everything that isn't a boardgame. Essentially, there are miniatures involved and the theme is generally conflict or war (though not always). Some people call this Wargaming, though that applies more to those who recreate historical battles.
I'm an avid tabletop gamer, preferring small scale miniatures that allow for large scale battles. Though I also enjoy the odd skirmish style game.
I started young, when I was 8, and was sucked into Games Workshop by my friends brother who was playing Space Marine 2nd Ed one day. I loved it immediately, though it would be a long time until I seriously collected. In fact, just prior to the release of Epic40k.
Nowadays I'm more open to other games, and will generally give most things a try.
Games
Epic (Space Marine, Epic40k, Epic Armageddon, NETEpic)
Epic is a 6mm scale war game by Games Workshop (one of the now unsupported Specialist Games), it is set in their 40k universe. This started me off in gaming, and I now own lots of miniatures - pretty much one of every army.
During my undergrad degree I found several like minded people and we played a lot of Epic Armageddon (EpicA), the latest version of the rules. I like the new rules, and I have been known to frequent the play testers forums - but sadly time and other things has led to a decline in how much I play.
I do however still attend Open War to play EpicA, a one day tournament run by the 1st Company Veterans at Warhammer World (Games Workshops Head Quarters).
Warhammer 40k
As a child I had a brief stint at playing this, but why play with thirty marines when I could get out my Epic and battle for continents?
Man'o'War
In the 'good old days' of Games Workshop, there were many other side games (rebranded Specialist Games some time in 2001, then promptly unsupported and effectively abandoned as of now).
I recall playing Man'o'War in my local GW Store, it was a lot of fun. Very Wargame like - there were lots of counters that you had to place next to units to indicate what was going on, and the ship cards... very clever game. Obviously I bought a fleet or two and was happy.
Sadly, in my naive youth I sold all my Man'o'War to buy more Space Marine. Then it all went out of production and I was kicking myself. Thankfully, in our modern world we have Ebay - where I spent a good few years re-collection several fleets.
Full Thrust
Full Thrust is a space combat game by Ground Zero Games. It's in its 2.5 Edition, and we've been waiting for the 3rd edition for a long time - I doubt it will come.
I loved this game because of its ship design rules (you can scratch build your own fleet - which I did, out of lego and wood) and its movement rules. It uses vector based movement... so if you thrust forward and turn the ship, in the next round you'll drift forward at the same velocity (speed and direction) unless you thrust again - which is what happens in space. Excellent - oh, and the rules are available for free.
Car Wars
An old Steve Jackson Games system, famous for having a complex car design system (you need to take account of the weight of fuel, and even add fire extinguishers). I only played it once a long time ago, but I recently bought the old CarWars Compendium 2nd Edition off Ebay - I purchased some old micro machines and am waiting to convince someone to play.
Hordes of the Many Things
By the Wargames Research Group, an interesting tactical system... unfortunately I feel the rules are awfully explained in the (very inexpensive) book. There are no races or species, each unit is a type and they are all the same for each player (there are heros, archers, spear, etc). The tactics come in how different types of unit interact. It's a fun little game, and you can play using any miniatures (if I find it, someone made a Narnia vs Never Ending Story battle which looked very good).
Warmachine and Hordes
A new kid on the block, Privateer Press, made their debut with Iron Kingdoms the roleplaying game quickly recreating all of that in a tabletop game.
The premise, every unit is broken in the right circumstance. It's a brutual game where one wrong move can mean defeat. I like it a lot, and I have a sizable Cygnarian army... but I'm hopeless at it. I think I've only won a handful of games.
BattleTech
I've only played a basic set, using card board cut outs, long ago; but I liked the system. Designing your own units was fun, and it worked for large groups... each of you controlling a single or pair of units. Would like to play again, but never found anyone willing to play.
Battle Fleet Gothic
A space combat game by Games Workshop, set in their 40k universe. The rules were interesting, the models looked amazing, it's unsupported now. A lot less fiddly than Full Thrust where you have a ship system sheet for every ship on the table, keeping track of all it's working guns, etc.