Here are some boardgames that I started off playing when I was a kid. An inconvenience of such games is that you can’t play them on your own, you have to find someone else to play with, which can be quite difficult if you stay at home often or have friends who aren’t enthusiastic in playing such games.
Generally my first boardgames were the roll-dice-and-move type. Depends a lot on luck and it may get boring after a while. Unfortunately this has become the mentality that most layman have about boardgames. Just like how cardgames equates to gambling.
Monopoly

This should be the most well-known boardgame in the world, with several editions and variations. I used to have the ‘Lion City’ edition, where street names are based on actual places in Singapore:

For your information, Geylang and Serangoon were the cheapest properties (brown) while Nassim Road and Queen Astrid Park were the most expensive properties (purple). Check the street directory if you don’t know where these places are. However at present, people would regard Marina Bay and Sentosa Cove as the most expensive properties, thanks to MacDonalds.
The flow of the game will depend very much on your die roll, which determines where you land. At the beginning, everyone would compete to finish the first round as fast as possible so that they can start buying properties on the second round. The rule of thumb is basically buy where you land on, since you’ll never know how often others will land on your property and pay you rent. If you can manage to secure all properties of the same colour set, you’re lucky. Otherwise if others manage to buy away one of them, you’ll (almost) never get a chance to complete the set anymore.
I had played the videogame version of Monopoly before, and the AI gave in too easily. I attempted to trade for a property that completes my colour set. Although the AI rejected my offer initial, it eventually accepted when I raised the agreed sum. Then I started building houses and hotels, and finally killed off the AI muhahaha.
The latest Monopoly Deal card game introduces a new dimension to how this property game can be played. Looks like the Monopoly legacy will always live on.
Scrabble

One of the most troublesome boardgames I’ve played IMO. It can be a big headache to calculate the points of every word formed, so I omitted the point system when playing in the past. Because of this, the game somehow became meaningless. Another tough part is trying to form the correct word. With limited vocabulary, we were often stuck with our letters. There were also frequent doubts on whether a certain word exists or not. Looking up the dictionary every turn was a hassle. In all, I actually disliked this game.
I think playing this game via the computer is much much easier. (eg. Playing online thru Facebook) Points are calculated automatically and you can just type the word in a box to search the dictionary.
Cluedo

A game with good theme but boring gameplay. Basically you walk around the mansion, enter rooms, find weapons and guess the murderer. The game can end pretty quickly if a lucky guess manages to strike. Moving from room to room is really uneventful and boring.
MAD Magazine

I think the illustration of that boy is really ugly.

So ugly that I used to get nightmares of him when I was small.
Anyway back to the boardgame, it has some really weird rules, basically opposite to that of Monopoly. You’re supposed to lose all your money instead. You move anticlockwise around the board instead of clockwise. Drawing chance cards can be quite punishing too. Although I only played this game twice or so, the bizarre rules (and illustrations) left an impression on me.
Super Mario Bros

I really liked this game a lot. The concept is similar to that of the videogame – destroy bricks, get coins and save the princess from the castle. Didn’t get much chance to play however, as this game belonged to my neighbor and some game pieces were lost.
Careers

Felt like an adult when playing this game haha. The aim of the game is to become successful in your career, while balancing love life and gaining fame. Sadly this is not easy to achieve in reality. This game was fun to play, but jotting down the love and fame points every now and then can be quite arduous, and it kills the pace of the game.
Trouble

The game is not as distressing as its name. Another typical roll-die-and-move kind of game, just that the die is not rolled, but popped by pressing the transparent shell in the middle. There isn’t much to this game; it can even be played on paper. Bought this as I was attracted by the commercial. Now you know why toys are so expensive.
Boardgames now have a different meaning to me, thanks to my platoon commander who introduced those non-typical boardgames (which can’t be found in departmental stores) and changed my mentality of all boardgames being roll-and-move kind that gets boring over time. Those games are generally not meant for kids and require a great deal of analytical and planning skills. The mind-stimulating factor of such boardgames is what makes them interesting and differentiates them from typical luck-dependent games where praying to the dice is often needed.