Even with one of the most stable operating system around, we all manage to run into trouble now and then. Sometimes, the simplest things work. Safari is my problem-prone app. I tend to only reboot my iMac when forced by a system update, and I generally have four or five apps that run all the time. Safari will reach a point where I get spinning beach balls with almost every page change. When that happens, I quit it, then restart it, and the problems generally go away — at least for a while.
If quitting an app doesn't fix the problems, try restarting the computer. Restarting fixes a multitude of problems. It gives the computer a chance to clean up those pesky cache files.
Company support sites and BBSs are a great place to look for help with a problem. If it is a common hardware or software glitch, those sites are the place to find fixes and/or work arounds. Apple has a great support board. It's generally the first place I look when having a problem. They have separate divisions for each piece of software and hardware. Usually, one of Apple's techs will answer questions posed there, but most are fielded by people who have run into the same problem. Much like our own iBBS, just searching by key words will get you an answer to your problem.
Of course, our own MacGroup iBBS should not be overlooked. I've seen questions answered in just a couple of minutes. Some questions take longer to answer, mainly because one or more of us are researching the problem. If you do pose a question on the iBBS, try to give as much information as possible. Operating system, amount of memory installed, app version number, what you were doing when the problem reared its ugly head, all of these things can help in coming up with the right answer.
Taking a cue from Calvin, before doing any software updates or upgrades, BACK UP! Things occasionally go wrong with updates. The system zigs when it should have zagged, and the upgrade kills something. It happens. If you have a fresh backup you can return to, you only lose some time. I have Time Machine running, and Deja Vu doing daily and weekly backups on a second drive, but I still do a separate cloned backup on yet another external drive before doing any major upgrades. (Yes, I'm paranoid about backups. I've had them fail.) With those automatic system updates, if something goes wrong, try downloading and running the latest combination update from Apple's download area. I've had that fix the auto updates that seem to have broken something.
If you run into a problem, don't panic. Think about it logically. What were you doing when it happened. What did you do just before that. Did you install something new. Take it a step at a time. It's never that bad.