Sure, it may seem like it crashed MySQL, and has been nothing but trouble since it came into your life, but trust me, you're going to want to give it a chance to explain itself.
The problem is, ibdata1 has the only key to your file cabinet. If you give ibdata1 the boot, it's going to take that key and swallow it (kind of a jerk move, I know). I mean, sure, you'll still know some information about what was on those files - enough to say "well I had this file.. and this file.. and those files looked kind of like this.." - but you're not going to have any of the paperwork to back it up. That makes them effectively useless.
So, if you do decide to kick ibdata1 out, you certainly can choose to do so, but just be aware that ibdata1 is a little crazy. It's done some bad things, and it isn't afraid to go back to prison. You are going to have to buy a new file cabinet, and write new files from scratch, unless you made copies of those files at some point and put them somewhere else, in which case you're golden. Afterward, though, you'll probably want to lay low for a while until the whole thing blows over, and avoid open areas or standing by exposed windows for an extended amount of time. Eventually, ibdata1 will probably get over it. Probably.
tl;dr - Removing the ibdata1 file is like removing all of your InnoDB-stored data. It will seem like it "fixed" MySQL, but that's only because it's literally loading none of your InnoDB data. You'll have a much higher chance of success if you try to troubleshoot the original crash/corruption issue.