You can also find sound libraries online. Some are free, Some you have to pay for.
Other than that, do some foley. Record all those sounds yourself. Think about what you want them to sound like and mic them accordingly. It's probably easier if you get some help with it, but it can be a lot of fun.
Get creative!

One of my old music tech teachers also taught sound design for film, and said that some of his students wanted a squelching sound for a door closing on an alien space ship, so they put a condom over an AKG C1000 and plunged it into a slush puppy!

You don't have to use sounds as they are either, you can time/pitch shift them, apply some fairly extreme EQ, modulation, reverse them, bit crush them and otherwise manipulate them to your heart's content!
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modulation and messing with the play rate can get that kinda thing. just play a power chord. now automate the play rate so it goes from 1x down to as low as it can go. power down! same thing, but the other way, power up!
Put a metal slinky up to your ear.
That's how they get the laser sound for essentially every cool laser gun.
Even better, put part of the slinky on a glass desk. It is now an amplified sound.

If you have a dollar store PC mic(I paid one dollar for mine at Dollerama) you can point it directly at a speaker and it creates some cool feedback sounds. Mine didn't even cause high-frequency. That's how shitty the mic is.

Old transformers pitch-shifted and stuff can sound cool too. Also, hard drives sound cool up close. May just be my 4Gb laptop hard drive.
..I was watching my death.
If you're after the blippy and trippy sounds of older gaming consoles (like the NES for example) then getting Plogue's Chipsounds is a must. Its emulations of the classic sound chips is the best I've ever heard. Just check the audio demos on their site. Use the SID settings and just smile all day.

For more life-like sound effects a good Foley library is the way to go. For shooting games you need a number of shots from the same kind of weapon so that things sound relatively natural (not to mention varying your ambience to match the surroundings) and then most free samples just don't cut it. There was a sound library I used in a commercial setting a few years back that was called something 6000. A ridiculous number of CDs that had too many sounds and ambiances to allow you to keep sane.
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