It does depend what you mean.
If you want to emulate a mobile phone for some reason, most I speak to wanting to do that want to play with various IM clients that want a mobile number to tie things to, then you can do that.
A lot of people wanting mobile emulators will be those doing websites and needing to check code. It is probably easier to use a website for basic checks and layout and save the hardcore stuff for a real device or some other thing. http://www.mobilephoneemulator.com/
is one of the ones I use.
You can also do things like http://www.android-x86.org/
and stick it in https://www.virtualbox.org/
(or whatever VM you like or I guess even hardware if you are so inclined) and get a lot of stuff done.
If you mean I want to play old games on my phone/tablet then things are kind of like they were on the original xbox and while 16 bit and older is pretty solid (more on that in a moment) things beyond that pose more problems but you can get some games going on. Technically there is a very impressive gamecube and wii emulator ported over and you can do very well on the PS1, not so bad for a lot of N64 things and I am not sure about the Saturn or Dreamcast but some things there too.
Some of the features are surprisingly advanced as well, and multiplayer wise can be more so, or at least considerably more user friendly, than some of the dominant PC emulators for a given platform. On the flip side the injection of money into this does mean certain systems, including those in the 16 bit and older and also often in the more obscure platforms where there might be less competition, may have their best option come via paid for emulators, this despite several of those being nearly untouched versions of popular PC emulators. I have not played with the big emulator frontend programs lately (never got along with them and as I can do better myself I do that, however RetroArch is a term you might want to start with if you do) but a lot of people go really into those.
If you mean I want to play 16 bit era games and http://arstechnica.com/gaming/2011/08/accuracy-takes-power-one-mans-3ghz-quest-to-build-a-perfect-snes-emulator/
is my jam then it is better than the PSP was but it is not that and you might still find kludges, frameskips and workarounds. Equally several of those existing ones will not be there and so some of the hacks that might abuse such things, also similar story for texture replacement hacks for things like the N64, will also fail to function as you might like.
To that end if you are thinking ultimate pre PS2 (plus GBA and DS) emulator station then not so much, though still pretty potent and certainly enough to be getting along with. I don't know whether the raspberry pi still tops it at this point but it is a strong contender if this is to end up under a TV and a laptop of any quality will walk all over it.
Most of the problems around here come from emulators making assumptions (I have had to teach people to hack or hack several games for the DS to allow people to use other languages as certain emulators assume it will only be that), issues with patching (people use these devices for their primary computing these days so when there are not ips, xdelta, bsdiff, ups, ninja and all the other formats we use around here patchers for any given version of android it causes problems), functionality differences (this emulator might have cheats where this one only has nice graphics filters) and people not paying attention.
If you are still recalling old articles where the DS and PSP, never mind what people doing stuff in the dingux/gp32/whatever worlds were doing, with their lovingly hand crafted emulators were walking all over android's "press compile and hope" ports of PC emulators then that stopped being a thing a while ago. You probably are going to want a controller though as it ain't like touchscreens are any closer to being a substitute for a controller yet. For my money the android crowd is still punching way below its potential for the power the hardware has, and is also a bit of tangled mess with all the charging and monetisation, but at the end of the day if you want to play old games you can certainly get it done.