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One of the great frustrations of electrical engineering is part obsolescence, price and scarcity. In accordance with engineering law, half of what's ordered is never used and the other half's not enough. The most popular style of EE hacking that I've seen is a pack-rat approach where everyone amasses 'a few of everything', perferably for free or scavenged. Granted, ICs are relatively cheap for their functionality, ranging from $.60 for a 555 to $15 for a high-speed digital signal processor, but they add up fast. (Especially since you'll need at least 2 of everything in case you short one out.) Passives add a few dollars too, and connectors can end up biting you if they're not spec'd well. And all that after dropping a few hundred dollars on a scope, meter, power supply, function generator and EEPROM programmer, not to mention the wire, boards, hand tools, etc.
In these days of low-cost, all-in-one Taiwanese epoxy-boards, just finding someone who will sell you "3 of those" can be a headache. Many hobbyists, myself included, are leaning towards "if you cant get it from Digikey, then I'm not going to design with it." Regardless, there are some tricks that can make your small-scale project easier to manage…
It's hard to go wrong with free. Parts manufacturers are often more than happy to ship you, for no cost, a few samples of their merchandise. They often ship within the week, sometimes the next day, and with free 2-3day FedEx/UPS.
These are only the half-dozen companies I've actually ordered from, if you know others, feel free to edit the wiki (or email me)!
The de-facto standard for annoying microcontroller design. Regardless, it's up there with the 8051 and AVR in popularity. It seems like you can get their more popular <$5 microcontrollers sampled. Also, of course, are their little flash memory chips, mid-freq RF chips and 'analog glue.' According to their FAQ, you can get 3 of 5 different parts, twice a month, shipped via 3-day.
Atmel Samples are shipped from distributors, but I've gotten chips successfully. I've even gotten engineering samples for unreleased chips!
Analog Devices High quality analog components, from the lowly comparator to the 60Ms/s D/A converter. Almost, but not everything, is available and I've found that sending a friendly email or calling them will net you what you're looking for. Unofficially, if its less than $10, it isn't a problem. The FAQ claims that Order limits are 2 of 3 parts, but there is no limit to how many samples you can request (although more than every other week is probably pushing your luck).
Maxim/Dallas Semiconductor DC-DC converters, serial line drivers, motor control, RF…Maxim specializes in "this part does one thing and does it they way you want it" chip design. If you want something analog, they've probably got it in stock. You'll need to log in first, but they'll send 2 of 8 parts (although I've never been turned down when asking for more) once per 90 days. I've received almost everything within a week.
National Semiconductor National makes the analog work horses of the industry, and they also have some nice DC/DC conveter and VCO/PLL design tools that do all that Ipeak math for you. If you're a student (or play one on TV) you can order up to 5 of almost any part, once a week. Usually arrives in a few days.
Fairchild Semiconductor The twin of National. You'll need to register but the only time I ordered something it was sent FedEx express and they didnt mind that I wanted 10. They have some policy, perhaps when you click on it, it won't say "updated soon."
Great things come from TI. More analog, of course. DSPs, some logic, battery management. You can sample anything off their big list. 8 different parts per order, with 1 each of the expensive stuff (like DSPs) and 3 each of the more common chips.
I believe you can order as often as you'd like. Boy, was I wrong: they'll put you on a blacklist if you order more than once per 90 days. eek.
Cirrus Logic Digital chips, D/A converters, Ethernet controllers, audio/video decoders, etc…Sometimes require a little encouragement/email to get their samples to you.
Linear Technologies More high quality parts, finally added 'one click' sampling for most of their electronics.
Freescale (previously Motorola) A variety of ASICs, microcontrollers, and other 'high function' semiconductors. Has a sample program (havent used it myself) where you can order 5 parts, 3 times per month.
Allegro Microsystems A smaller manufacturer of mostly DC/DC converters, you can sample from their website
Philips Semi Lots of chips many ASICs, you have to call the regional sales office to get parts.
ST Microelectronics "ST will happily send you up to 7 different samples for free. Quantity for each chip varies (I got anything from 3 to 5), and you have to register and provide some semi-credible excuse on what you intend to do with the goodies. If you're into audio, you could do worse than use STm's chips." - Luca R.