First and foremost: most of this content is not original. I've found a few great blog posts on the internetz that have Electronic Workbench suggestions. However, Instructables does not allow me to add random links to a collection. Therefore I am citing these great posts:

Each step will cover a blog post.

Step 1: Jayson Online

EEVblog is an awesome blog and YouTube channel (you should subscribe.) David rattles off a detailed equipment list that borders on the medium to high-end range & is transcribed by Jason Online. Here's what he suggests:

2 Multimeters to measure current/voltage at the same time (Extech EX330 and AM-510). Extech has micro-amp range and temperature sensor. Get a thermo probe as well. – $100
Get a pocket multimeter and voltage detection probe (EX330 comes with non-contact voltage detection unit which lights up near mains)
Digital oscilloscope (Rigol DS1054Z) – $400
CRT analog oscilloscope, 20Mhz dual channel – $50 to $100 for a second hand one
Function generator for creating signals (Instek GFG-8219A for analog or Wavetek model 22 or Instek SFG-1003 for digital) – $150
Power supplies (more than one is recommended, dual tracking fixed or variable supply, constant current setting, build one yourself – high power stuff is usually not needed) – $100
Soldering iron with soldering station (Hakko FX-888D or Hakko 936 with a variable temperature setting, use a chisel type tip for soldering iron) – $120
Hot air rework station (Atten 858D) – $60
Solder (standard 60/40 multicore, use thin solders with less than 0.5mm diameter. Solder spool stand and solder wick is also recommended) – $20
De-soldering pump – $5
Flux pen – $5
Tweezers (get stainless anti-magnetic ones, and get a set with varying tip shapes) – $10
Get a pair of goggles and fume exhauster or a simple desktop 12v fan for safety - $10
Magnifying glasses preferably head mounted (for example, to inspect solder joints). If you are getting magnifying lamps, get a 5 diopter one – $25
Assorted set of connectors – $20
Assorted set of side cutters – $10
Assorted set of pliers – $10
Get a decent combination wire stripper or use side cutters – $10
Small size spanner set and Allen key set – $10
Hot cgue gun – $10
Assorted set of small files & and a nibbler – $15
X-Acto knife – $10
Engineering ruler and digital vernier calipers – $20
Assorted set of screw driver kits – $50
Magnetizer/demagnetizer for screwdriver and crimp terminal connectors – $5
Assorted set of clips (banana plug, alligator clip etc.) – $30
Tapes (duct tape, cello tape etc.) – $15
Assorted set of wires –Standard double size breadboard with pre-shaped jumper wires – $30
Strip boards with strip board cutters – $20
Electronic cleaning solvent and air duster – $10
Electronic component kits (resistors, capacitors, LEDs, chips etc.)
Anti-static work mat/ anti-static wrist strap – $20

Step 2: The Life of Kenneth

Kenneth Finnegan also has a great post with links directly into Amazon. Here's his take on an equipment list:

Equipment

Needle nose, pliers, and wire cutters
Flush cutters
Tweezers - Also get plastic ones if you're doing chemical PCB etching.
Dental picks - Very nice for scraping, poking, prodding, etc, while soldering.
Wire strippers - You'll usually see people using the combination wire strippers / crimpers. I wasted too much of my life dealing with these before realizing how much better real wire strippers are.
Hot glue gun - Super useful for assembling prototype cases, insulating stuff, etc. Just don't put it on anything that dissipates power like a linear regulator.
Blue tape - For crudely insulating joints, holding things together, and being a marking surface for hole positions on black plastic.
Screwdriver
Breadboards - I would buy a few columns more than what you think you need, because running out of space half way through a project sucks. I have 5 single column boards, a two column board, and a 4 column board, which is a little excessive, but I got good deals on them from friends not wanting them after our college electronics classes, and it's nice being able to have a few different prototyped projects sitting around at once.
Breadboard wires - These are reusable, but at some point you do need to start culling the used ones and replenish the kit.
Clip leads
Coin envelopes - These are surprisingly useful for storing different values of resistors, or diodes,or anything else tiny.
Altoid tins - I love these tins for basic project boxes, as well as storing bulkier components such as transistors and crystals.
Solder sucker / Solder braid - Once you start soldering parts together, you're going to start making mistakes soldering parts together. These undo those inevitable mistakes.
30x Jewelers loupe - I use this ALL the time to check for solder bridges and cold solder joints.
Volt / MultiMeter - Repeat after me: do. not. buy. the. $15. one. at. the. hardware. store. Also make sure you have a spare fuse in stock for this. You will only ever blow your amp meter fuse when you're using it.
Test leads - Volt meters do come with a set of test probes, but it's worth investing in a seperate kit that has all the interchangeable points (microclip, spades, alligator clips, etc)
Power supply - I managed to find a nice power supply where someone mounted an ATA computer supply in a box with screw lugs for 3.3, 5, 12, and -12V. You can go for a fancy variable supply, but I didn't. At the very least you'll want a nice breadboard power supply and a 9V wall wart.
Banana plug test leads (to alligator or mini-clip) - I use these to connect projects to my power supply more than anything else, but they also plug into the posts on the top of all mounted breadboards, so they have all kinds of uses.
Soldering Iron - I own the last generation Hakko 936, but it's safe to assume the more recent 888 model is just as good. The difference between a $20 soldering iron and a $100 soldering iron is amazing. Being able to turn the iron down to 300C and not worry about destroying PCBs makes soldering a lot easier.
Tip cleaner
Fine gauge solder - I use .032 diameter solder, and even that is a little thick some times; the finer the better. I also have some 0.1" solder for bulk heat-sink or strain joint soldering, but its use is rare.
Helping third hand - When you're soldering, these are priceless.
Calipers - I use these more for my mechanical engineering projects, but is still useful for measuring clearances and pitch.
Oscilloscope - The holy grail of the hobbyist shop. Consumer scopes have finally gotten to the point where they're reasonably priced and GOOD. A lot of companies have started coming out with toy USB or iPhone oscilloscopes, and I'll just remind you that they really are just toys. Remember that the scope isn't going to do you much good without probes, so do some research and pick out the specific probes and cables you want to use with your scope, and expect to spend some money on these as well, because a good scope with bad cables is going to waste your time.

Components

10x each size of 5% 1/4W resistor: 100, 330, 1k, 4.7k, 10k, 100k. - Now this is incredible sparse, but is plenty for digital, where you just need current limiting and pull-up resistors, so if you instead want to just buy a complete kit and be done with it, that wouldn't be a bad decision.
10x each capacitor: 22pF, 0.1μF, 100μF. - Digital really only needs a single value for every few decades. Any analog work will require a much larger variety of cap values, so again, if there is any interest, feel free to buy a complete kit.
1x 500μH inductor for buck charge pumps.
5x 8DIP, 20DIP, 28DIP socket
10x 2N3904 NPN, 2N3906 PNP transistors - I also have higher power transistors and MOSFETs for heavier duty, but these will get you far in driving a few LEDs. As far as higher power ones, good ones to start with would be the 2N2222, and then probably go to the MOSFET IRF820.
3x 2N7000 - MOSFETs are interesting because, unlike bipolar transistors, they are voltage controlled instead of current controlled, which is sometimes useful when you need control signals with very little power behind them. I've never done anything with P channel MOSFETs, but ZVP2106A would be a good FET to get you started playing with those.
10x 1N4007 - High power diode. Most applications will require less than 1000V reverse-voltage, but it's easier to just stock one diode that can handle everything, than to try and save a few cents by using 1N4002 in one project, 1N4004 in another, etc etc.
10x 1N4148 or 1N914 - These are the classic small-signal diodes, that don't handle current well, but are useful for diode logic and signal isolation.
Quartz crystals: 32k, 16MHz - These are for precise clock sources for time-critical projects like clocks or high-speed serial communication. Microcontrollers particularly can choose between running off a crystal and running off their internal oscillators, but it's the difference between them being a few percent accurate, and them being 20ppm (0.002%) accurate. Particularly for the 32k crystal, the load capacitance can be important, so check to see if your application needs the 6pF or 12.5pF variants, or else it might be a little off frequency. Between the DS1307 and MSP430s I use, I only ever need the 12.5pF one.
7805 / 317 - Linear voltage regulators aren't very efficient, but easily let you take something like a 9V battery and turn it into the 5 volts digital circuits need. There are better, more modern regulators, so be sure to browse manufacturers websites for such.
5mm LEDs - These tend to be available in bulk bags on eBay, etc, so getting a bag of 100 will probably save you quite a bit of money if you ever think you're going to build something that uses more than one or two.
Copper clad perf board - For when you want to solder down your prototype after breadboarding it, but don't want to make custom circuit boards. Many beginners also like the breadboard shaped perf board, which allows you to copy point for point the circuit you built on your breadboard.
22 gauge wire - I got a huge spool of this at the hardware store before metal prices took off 10 years ago, but even just getting a few dozen feet would be plenty for breadboarding and small projects. Getting 22 gauge is important, since 20 gauge will damage the clips in breadboards for being too large, and 24 is a little too small and will tend to fall out.
Male and female header - These are rows of pins and sockets that can plug into each other, or can be used as connection points for jumper wires. You can buy them in the specific lengths you need, but male header is designed to snap apart, and with female header you just crush the next socket over with wire cutters to cut them to length. Male: straight, right angle, Female: straight, right angle.
Push buttons, switches, DIP switches, etc
Fun displays - Seven segment LEDs, dot matrix, HD44780 family LCDs, etc. I've got a whole box full of various segmented and matrix displays I've collected over the years both online and at salvage shops like Halted. You'll save a lot of money getting these things on the second markets, so I'd urge you to spend some time looking through them for inspiration, instead of looking for a specific display.
Batteries and battery clips - The common standard for 5V projects is using a 9V battery and a 7805 regulator, but the small capacity of 9V batteries always bothered me, so I prefer AA clips, but do use both.