The first handhelds were these LED light arrays overlayed with different painted designs like the different sports fields. I played all three of the ones shown below which came out in the late seventies alongside Atari 2600 and then Intellivision in '79. Me and my neighborhood friends played the heck out of these things to the point where we wore the buttons right off and the casings were so beaten up, the circuit boards showed through. I picked up these again off of ebay a few years ago for nostalgic reasons. 
Then I came across some more handheld ads from 1980 with this Parker Brothers Wildfire Pinball handheld which I never knew about.
And this Bandai America Electronic Marvels handhelds ad, also new to me.
Then I used to play around with my scientific calculator, a TI-55, as if it were a game machine. You could do simple programs on it. It seemed like an improvement on those simple LED games, but there was very little entertainment to be gotten out of it. After all, it wasn't supposed to be a game machine, but you had to think of something in between classes.
Interestingly enough, Gunpei Yokoi was apparently inspired to create Game & Watch by seeing a business man pushing buttons on a similar calculator. I found this ad for Game & Watch, begun in 1980, below in a old comic book. I never owned one or even knew these existed until recently. I guess I never knew anyone who had one or maybe they were only in the toy store which, me being a teenager, I didn't frequent. Anyway this had an LCD screen which is a much better choice than LED arrays. You can do so much more. No wonder it became the standard for handhelds.
So those were what you had until the release of Game Boy in 1989.
"Space age electronics"
Sigh, old advertisements were the best!
I can't get enough of them.
Oooh I had that football game.
That football game was owned by my then best friend and next door neighbor and I used to go over there all the time and we'd play it. That thing was so beat up after a while, I'm not sure how we still played it.
I'm also not sure how that game was fun anymore. I gauruntee you that it ceratinly was though!
Yea, it's amazing we got so much out of a bunch of blinking lights.
I also remember having Tiger Electronics. Plus, skip to my middle school in the 90s, and the TI-83s had Mario and some sort of puzzle game on them. I didn't have one of the ones with those actual games on it, though. All the Advanced Math kids did.
It's pretty weird. Scientific calculators were like a cool thing to have when I was in high school.
I found this handheld museum site with all the Tiger Electronics games on it here: http://www.handheldmuseum.com/Tiger/index.html
That actually helps me a lot with a project of mine, thanks!
That site was cool! Some of those Tiger handhelds were works of art like the Castlevania one. A perfect thing to have for a Castlevania fan.
If I remember right, that Castlevania one is really rare.
I wanted some of these early handhelds as a kid, but I never got them. Except for a Pac-Man game that was made to look like the arcade cabinet. I got that one for Christmas one year as a kid.
Those table top arcade cabinet games are pretty neat. I'd like to have one.
I had the classic football. but if I remember right, the case was green?
Like this one? It was Classic Football 2.
.
Also, this is a cool website I just found: http://www.handheldmuseum.com/Mattel/FB2.htm
Yeah...that's the one I had
Man i had all of these hand helds and i had the Texas Instrument Calculator god i feel old now lol!!
It's amazing how much I got out of that Mattel Electronics Baseball. I could hit home runs at will in that game.
The Coleco ( spell check ) we took on road trips and i know that beeping had to drive my dad crazy lol!!!
I never liked these things as a kid but I grew up with the Game Boy, so I guess I was already spoiled lol. Even on the Game & Watch collections, I always prefer the modern renditions of the games. I was one of those kids, though, with a TI calculator in high school that had that Mario game. Beat that thing so many times lol
The GameBoy was such a huge improvement.
The lonely rich kid who lived up the hill from me when I was 12 and lived overseas had a bunch of the Game & Watch games. I was very envious.
Game & Watch was another thing I knew nothing about in the eighties. Funny, they were really popular.