Rosio Pavoris

Nearly all cultures have historically used numeral systems in base-10 (that is, the decimal system) or some multiple thereof (Mayans used base-20, Babylonians base-60), supposedly because a human hand has ten fingers.¹ If that’s the case, the ancients suffered from a severe lack of imagination.
If you count on your fingers in base-1 (that is, the normal way), you can count to ten. However, there is a way you can get up to 1023 using just both of your hands.

How? Use binary, of course.

It’s actually really easy once you get used to it. If your finger is up, that bit is set. If it’s down, it’s not.
For example, the following are the numbers 0, 24, 17, and 31 (only one hand is shown, because it’s easier; 31 is the highest you can go on one hand, obviously).²

Counting on your fingers in binary is a skill well worth picking up, especially if you intend to use computers more often than never, but also just because.
You can even count with negative numbers, if you use two’s complement or similar.

It might be harder to expand this to also use your toes, but every toe you add doubles your range of numbers (you can count up to 2ⁿ - 1, where n is the number of digits; including 0, that means you can represent 2ⁿ numbers), so you probably wouldn’t need all of them. If you’re counting up to 1,048,575 (or 2,097,151 if you’re a guy, hurr), you’re better off grabbing a calculator anyway.

¹ The Native American Yuki tribe actually used a base-4 system, because they counted the spaces between the fingers of one hand, which is interesting. Some Nigerian tribes use a duodecimal system (that is, base-12), because they are mutants.
(Actually, base-12 exists in a lot of places, mostly in the Imperial system of measurement (twelve rods to a hogshead, and all), and in various forms in time-keeping (twelve zodiac signs, twelve hours on the clock).)

² These hand pictures are actually repurposed from a chart detailing some variety of sign language.