4026 + 7-segment display: do I need transistors?
Life can be tough. CMOS ICs from the CD4000 series, like the CD4026 can only source and sink very little current, typically 1 mA at 5 V and that will be much too little for a typical 7-segments display. So I'm afraid you'll need the transistors, especially since you're now already asking for more brightness.  

But You don't necessarily need all these discrete components. A ULN2803 replaces 8 transistors, so you'll need 1 IC per display. Important note: I just read that your displays are common cathode. The ULN contains an array of NPN transistors, switching to ground, so they can only be used with common anode displays. 

edit
starblue found a high side version of the ULN2803 in the UDN2981, so this is suitable for common cathode displays. I don't know about availability; Digikey lists only two versions, both from Allegro, as as non-stock, call for price.
Inputs are active-high, so it can be driven by the same devices which would control NPN transistors or the ULN2803.
end of edit  

Alternatively you may use low-power Schottky ICs, but then you'll need the counter and the display decoder separately; I don't think the combination like the 4026 exists in LS-TTL. The 74LS90 is a decimal counter, and the 74LS247 a 7-segments decoder, which can drive LEDs directly. This is also an active low output IC, which means common anode:-(.

Other solutions you've seen requiring less transistors may have used a microcontroller and a multiplexed display. Then for 6 digits you'd only need 6 + 7 transistors, instead of 6 \$\times\$ 7.