Have you ever grabbed Bowser out of his recovery? It's pretty cool.
I've done it to DK a few times, but it was totally by accident. You need almost flawless spacing to grab DK's aerial Up+B. Why am I talking about grabbing moves you'd never want to grab? I have no idea!
Anyway, to address the purpose of this thread, yes, you should grab with Yoshi, just like you should grab with every character. I can't think of a single character in the game that doesn't have either a good throw or a viable combo/KO option after a throw.
Yoshi's combos are best started off with grabs because the throws you'll be using (up and down) render the enemy at an almost perfect height, no matter their constitution or percentage. The very least you'll be able to do is an Egg Toss or an up aerial and even these options are a free ~10% (not counting what those moves can lead into on most characters at most percents). Shieldgrabbing is best against dash attacks (Samus, sometimes Peach if they don't space it, definitely Sheik, and Marth if you can time it right). You can also shieldgrab wakeup attacks quite well as long as you know which direction the character will strike first.
You really shouldn't be shieldgrabbing aerials too much. If anything, roll away, lightshield the aerial (I've been lightshielding so much more now, it's amazing), or maybe drop the shield and jab. You can even supershield or just keep the shield up.
Uh...dash grabbing is good, provided you learn approximately how to space it. Grabbing characters out of the air is nice, but that provides more than its fair share of risk. This is most easily done against Fox/Falco/Falcon at ~110%. You can up tilt and then grab them before they can recover, provided you have an idea of which way they'll DI. You can also try some timing tricks with standing grab. Since most characters have a rather quick standing grab, you can bait a dodge from your opponent that is anticipating a standing grab (but who is too used to the timings of grabs from other characters) and standing grab during their dodge to catch them while they're vulnerable.
I could go on and on, but I'll wait for some input from others before I drop my usual page-long posts. =_=