Upgrading CPU for a Socket 1155 LGA

i7-3770K, but it will not be worth the money

I disagree, the i7-3770 (k or not k) is still a very very good CPU, the additional cores over the 3220 will give some benefit, almost as much benefit as going to a new platform, but without the additional cost of RAM and Mobo.

an i5-3570(k) would be nearly as good and cheaper.

I agree fully that it is an excellent CPU. HOWEVER, I highly disagree with the decision to purchase one at this point in time, these CPU's are very old and you will be paying near full price for a heavily used CPU which may have been overclocked to hell and back and may even be at the end of its useful service life. Who knows how much longer these things are going to last? I myself am still running a i7-2600 and silicon is silicon, it degrades over time. I can not bring myself to advise you to buy one.

Well, first of all, what motherboard do you have, as that could potentially put some limitations on the available CPUs.

Secondly, if considering a new CPU, only pick a "K" version if a) your motherboard's chipset will support overclocking and b) you plan to buy an aftermarket cooler (air or liquid) to OC the chip. Although the "K" models may have a slight frequency bump, it's usually not significant enough to get any advantage unless you're going to OC it -- & that assumes there's even the 'bump'. For example, the i7-3770K is slightly faster than the i7-3770 (3.5 vs. 3.4 GHz), but aside from the OC potential there's no difference between the i5-3550 & the i5-3550K (both @ 3.4 GHz).

That being said, a CPU upgrade probably wouldn't hurt. Unless you're playing games that don't require a lot of CPU horsepower, or playing older games that really don't use more than 2 cores, you still have some CPU choices that would move you from 3rd-tier (your current i3) to 1st-tier (http://www.tomshardware.com/reviews/cpu-hierarchy,4312.html). As I said before, your actual motherboard model could potentially limit the available CPU upgrades available, but if they're on the list of compatible CPUs for your motherboard you could easily pop in an i5-3550 or -3570, or even an i7-3770.

EDIT: Apparently a bunch of us were posting at the same time. Just one thing to add: never buy a used CPU. It's one thing to get a used CPU from a friend or family because they just updated their old system/bought a replacement system, & it's now just sitting around. It's another thing to buy it sight-unseen from a stranger online. Although my local Micro Center doesn't currently have any LGA 1155 chips in stock, it does have some Ivy Bridge Xeon chips (1 LGA 1150, 2 LGA 2011), & all 3 are brand-new (not open-box, not customer returns, but never-used, brand-new).

Which brings up another option: Xeon chips. Anything from the E3-1230 V2 to E3-1290 V2 could (potentially) work as a good upgrade: same or faster core speeds, & more L3 cache (8MB; not only a lot more than your i3, but more than the i5 chips). Again, just make sure the board is able to use it.

Buy a non-K and you won't have to worry about its overclocking history since it cannot be overclocked by any meaningful amount. With abuse mostly eliminated from the equation, you can expect the CPU to last 15-25 years.

I have never had a CPU fail on me and the oldest working PC I currently own is over 15 years old (Coppermine Pentium 3) with about 10 years of 24/7 operation, the first half of which overclocked from 650MHz to 800MHz.