You need BP511A for your camera... which are very common, so you'll have tons of options.
There are some semi well-known battery clones that are at least as dependable and have a warranty at least as good as Canon's. Sterlingtek is one of the best, has a full warranty and appears to honor it. Those can be bought direct or found in some stores. Large retailers such as B&H and Adorama also offer third party clones and either back them with their own warranty or with a manufacturer's warranty.
Those will usually cost you about half what Canon charges for theirs.
If you want even cheaper, there are all kinds of truly generic clones on eBay and elsewhere. I bought a handful of those a few years ago and they worked fine, but it's questionable if there's any warranty... at least for more than 30 seconds or 30 feet or 30 clicks, whichever comes first.
I bought no-name clones in batches of four or more and paid $6-8 apiece, including shipping (Canon were about $45-50 + shipping at the time). Never had any problems with them at all. They were higher rated than Canon, in fact.... but in use I can't really say that they gave more or less shots. Never really compared them... just used them without any problems.
I wouldn't hesitate to buy cloned BP511/511A again. After all, they are just rechargeable batteries.
I can't say about other types of electronics. I seem to recall replacing a cell phone battery with a cheapy at one time, and not having any problems. But don't really have enuf experience to say one way or another.
There have been "horror stories" of battery meltdowns, even to the point they ruined the gear they were in... but I think those are pretty rare, all in all. If you look at Canon batts, they say "Made in China" on the side, same as the clones. I wouldn't be surprised if the OEM and clones came off the same assembly line and the only difference was the name printed on them.
It's a separate issue... But someone looking for and paying for OEM should be careful about knockoffs. If you are paying extra for the brand name, you should get the brand name item! I think there were some fake LP-E8 or something, going around for a while.
And, the newer LP-series lithium batteries Canon is using in more recent camera models are a bit different (from the earlier BP-series). There are some good clones of these available, too. But there are also clones that don't include the chip that gives more info on battery status and usage in the camera, and/or can't be charged in the Canon chargers. Just have to be a little more careful when buying these.
