It's easily done. I blew one up by leaving it on OHMS after checking the resistance of an element, and then checking for voltage on the appliance with out changing the dial to AC voltage. This was a fair few years back, and luckilly I had bought a half decent meter made by 'Di Log' and it was fused.
I would suggest that if you do buy a cheap meter, you buy some expensive and preferably fused leads for it. So if you do put some voltage on it that you shouldn't, it doesn't blow up in your hands.
The fuse exploded inside mine. Didn't just blow. I took it apart, and shook the glass out, put in another quick blow, low amp fuse of the right rating and it was fine for years after. Decent leads can be used from meter to meter too. Unless you damage them.
I know have two meters. One that stays in my van, and one in with my analyser. The one that stays in the van is a Socket & See one. Gas Man (mod/regular on here) had one of these, and didn't rate it. I've found it ok.
The other is a Fluke 116.
It's handy to have something that can measure micro amps, though I don't use that function very often at all. You can test flame rec probes, and thermocouples with that setting.