Having played a lot of competitive battles since writing this question, I have since learned of many Not-Fully-Evolved Pokemon which can be competitively viable due to differing abilities or good (enough) stats. Hell, a Follow-Me Magmar was on a team that won the VGC Worlds Championship in 2013!
Most of them will run Eviolite, which boost a Pokemon's Defense and Special Defense and allow it to compete against it's evolved counterparts. Note that this boost is calculated on the final stats, which includes Natures, IVs and EVs, not just the Pokemon's Base stats!
There are many not-fully evolved Pokemon that are competitively viable in their current form. Here are a couple of the more popular ones as an example:
Chansey evoles into Blissey in Generation 2 and up with High Friendship.
Chansey's HP is only 5 base stats less than Blissey (250 vs 255), and with Eviolite doubling it's calculated Defense (which includes Nature and EVs as well as the Base Stats), Chansey is better equipped to deal with Physical Attacks, an area that it's counterpart Blissey is usually lacking, which chooses instead to focus on it's higher Special Defense.
Porygon2 was introduced in Generation 2 as an evolution of Porygon. As of Generation 4 it received it's on evolution in Porygon-Z (when traded with a Dubious Disc).
With Eviolite and Recover, Porygon2 makes a very good wall that can support the team, usually setting up Trick Room and threatening with Ice Beams and Thunderbolts/Discharges. Porygon-Z on the other hand is usually built to be a very offensive Pokemon in a Revenge-killer position
Togetic evolves into Togekiss in Gen 4 and above by way of Shiny Stone.
Like Chansey, Togetic focuses on more defensive bulk than it's evolved counterpart, with a lot of Togetics absorbing attacks for their partners with Follow Me. They can also harass with Encore/Thunderwave and support the team with Tailwind.
As of Generation 4, Murkrow evolves into Honchkrow when a Dusk Stone is used on it. The main reason why Murkrow can be competitively viable is in it's Hidden Ability: Prankster, which gives Status moves used by it a +1 Priority. With it's access to a wide variety of Status moves, Murkrow to act as a viable Support Pokemon, especially in doubles.
- Speed-control with Thunder Wave/Tailwind/Quash
- Harass with Taunt/Torment/Swagger/Flatter/Confuse Ray/Feather Dance
- Set up (or cancel out) weather effects with Rain Dance/Sunny Day
- Stall out opponents with Toxic/Roost Paired with Substitute or Protect
- Perish-Trap with Mean Look/Perish Song
- In a pinch, it can also hit back with Foul Play or Sucker Punch
These are just some of the Not-Fully Evolved Pokemon that can hold their own in a competitive situation, there is also Rhydon, Magmar, Electabuzz, Clefairy, Golbat, Scyther, Doublade, Piloswine and many more.