Is a function generator necessary for every day lab use, or is it special purpose equipment? That is, does it have similar utility to an oscilloscope, or multimeter - would you use it regularly enough to justify it's cost?
If you're working with digital systems and square waves/pulse trains only, then it's probably not necessary. However, for analog amplifier design (ex. audio), it's an imperative.
If you haven't been stymied on a project because you lacked this tool, you probably don't need it. Spend your money on an oscilloscope and logic analyzer instead. Conversely, if you can't imagine why you would need a logic analyzer, you should spend your money on a function generator.
Depends on what waveforms would be useful in everyday work. I like to play with waveshaping and signal processing, so a good versatile function generator is one of my favorite instruments. It's likely to be useful for almost anyone into electronics who's gone beyond building crystal radios and blinking LEDs. A more important question is: which waveforms will you need, and at what quality?
Sines are good for testing linear filters, taking measurements at specific frequencies. For accuracy, the sines have to be low distortion. Less expensive generators have poor sine waves (look at the THD).
Triangles and squares are good for testing amplifiers - our eyes aren't sensitive to small deviations from a sine, but are very good at seeing problems with straight lines and square corners.
Ramp waves are good to sweep oscillators over a frequency range, which is also good for testing linear filters, and also circuits like mixers, modulators/demodulators, and audio testing.
If you're into experimental physics, pulses that you control in fine detail can be useful in controlling equipment, data acquistion, strobing to observe fast repetitive phenomena.
In most cases, for serious accurate work there are specialized instruments for the job, but even with a budget for such things, a function generator is useful for quick and dirty experiments of all kinds.
This all depends on what work you are doing. Some people don't even need a scope or a dmm.
More generally, some people will say its not worth getting a computer (even some EE's), yet I am sure most of us would argue it is worth it.
So what work do you do that you wish you had a function generator? If you can't think of anything then it's not worth it.
I found a fairly cheap one for $153: http://www.bellnw.com/products/0762/
It's pretty much no-name but it will certainly be quicker for me to use as the PWM input to a breadboarded switch-mode power supply than rigging up something with an Arduino and op-amps. Plus, only $153. That's an expensive dinner for four, or a couple of outfits. If you'd buy a $1k plus scope, buy this, no question.
EDIT: It may be worth it to get the SFG-1013. It has a voltage display.
A software DDS with a suitable MCU is a low-cost way to make a function generator. This design of mine will go up to 200 kHz or so.
As far as a good all-around tool, I've had pretty good luck with the National Instruments myDAQ (not an advertisement, we bought a couple to evaluate for our EE department). They can be had for 175 dollars with the educational discount, and it covers most of the basic needs. It is basically a function generator, an oscilloscope, and a multimeter all in one.
The analog output (function generator) operates at up to 200 kS/s, meaning that you can pretty accurately generate waveforms for the audio spectrum (I believe that the software allows up to 20kHz). Much higher, and you'll have to shell out more money. The feature that I like is the arbitrary waveform generator, which can be very useful depending on the circuits that you are building.
Basically, the need for most test equipment is determined by what sorts of projects that you are working on. If you are doing hobby-level projects, you may not need any sort of expensive hardware.
As a relative newbie into electronics at a later point in life, I concur with the myDAQ suggestion. You also get LabView with it that is very robust plus a ton of other benefits and features including MultiSim. This doesn't even scratch the surface.
TechShop (www.techshop.com) opened a location near me late last year (Austin/Round Rock location), and they have them available at the educational price and also have training classes. In addition to all of their other tools and machinery, there's also an electronics lab there with scopes, function generators, most of the usual bench equipment, a small re-flow oven and a little ShopBot for making PCB's, just to name a few.