I used to play darts and even had my own set, which were black with black flights. Someone once said they looked like something out of Star Wars - as used by Dart Vader, I replied. My playing, like the joke, wasn't very good.
Chess and draughts are other games I've played in pubs, and although I enjoy a game, I am, again, not very good at either. I've seen backgammon, but I've no idea how to play it, but as it's associated with gambling, I'm not likely to find out as gambling has never interested me.
Table skittles and shove ha'penny are games I haven't seen in pubs for years, although dominoes can sometimes be found still. Table football was very popular in our student bar, and I did become quite adept, often taking on two opponents single-handed and beating them, which actually isn't quite as impressive an achievement as it sounds, but it looked good.
Very few pubs today still have full-size billiards tables, probably because they take up so much room. The last time I had a go, which was in a pub in Warrington, I couldn't get the hang of it at all - the level of skill required is far higher than pool, and certainly much higher than my ability. I did use to play pool a lot, although I wasn't very good, although one Saturday afternoon in my (then) local I beat all comers for about 3 hours, and in a pool competition at work, I once lost the game on my last shot in the final: I completely missed the black that I was trying to pot. My opponent had already started walking to the bar and had to be called back to take the final shot, and win the cash prize. Generally, though, my tenure of the pool table tended to be short.
I'm glad that quite a few pubs still have bowling greens. I remember when we students would go to the Plough in Houghton Green near our college and occasionally have a game of bowls. Although we enjoyed ourselves, the old fellows watched us and had a good laugh at us hippies (as they thought of us) being utterly useless on the bowling green. Still, it was nice way of spending a sunny afternoon, especially when you were supposed to be in a lecture.
A game I've only come across only in one pub was pétanque, in which you throw metal balls on a gravel pitch and try to get closest to a jack; it's also sometimes called boules. Another good summer game, but the pub concerned doesn't have the pitch anymore.
The key point about all of these activities is that they are social; you play them with other people, and you can still have a pint and a chat. Games machines, on the other hand, are solo activities: the companions of the player are reduced to spectators and often have to remain quiet so as not to disturb his or her concentration. They're not sociable activities and don't really fit into the pub ethos; their natural home is the amusement arcade. Proper pub games should enhance your enjoyment in the pub, not restrict it.