We all know CO₂ as a waste product of metabolism . Does CO₂ have any helpful role , apart from having a role in pH of blood ?
Before I restrict the answer to human metabolism, I recon it is important to mention that CO2 is the source of the carbon atoms of glucose in photosynthesis (in the Calvin cycle). [In photosynthesis CO2 is 'fixed'].
Even with the above restriction, I am certain I cannnot do justice to every helpful aspect of CO2 in mammalian metabolism, and I'll restrict myself to just one area that came to mind on reading your question: the requirement for carbon dioxide (in the form of bicarbonate) for fatty acid biosynthesis (FAS) and, in a bit more general sense, mammalian/bacterial biotin-dependent carboxylation reactions. Depeding on other contributions, I might be able to extend this a bit later.
Salih Wakil showed that CO2 is an absolute requiement for fatty acid biosynthesis, but carbon atoms from CO2 do not appear in the fatty acid product.
We now know that FAS begins with the carboxylation of acetyl-CoA to malonyl-CoA, catalyzed by the enzyme acetyl-CoA carboxylase. Acetyl-CoA, ATP and bicarbonate are the substrates for this enzyme, and malonyl-CoA is a key product. One of the many interesting properties of this enzyme is that it contains biotin, which (in this case) may be considered a carrier of 'active' CO2.
This explains the requriement for carbon dioxide but why no carbon from CO2 in the final product?
It is now known that in subsequent FAS reactions, a derivative of malonyl-CoA condenses with a derivative of acetyl-CoA (I am simplifying here) to give a four-carbon compound with loss of CO2.
Thus, carbon dioxide (in the form of bicarbonate) is an obligate requiement for mammalian fatty acid biosynthesis, but no CO2-derived carbon is incorporated into fatty acids.
Carbon dioxide is also required for oxaloacetate formation from pyruvate. This reaction may be though of a method of 'filling up' a key Krebs Cycle intermediate (a so-called anapleurotic reaction). The enzyme here is pyruvate carboxylase and the substrates for the reaction are pyruvate, bicarbonate and ATP, with oxaloacetate being a key product. This enzyme also contains biotin and (like acetyl CoA carboxylase), CO2 becomes covalently bound to biotin during the reaction cycle.
Pyruvate-CoA carboxylase was discovered by Harland.G Wood and C. Werkman in bacteria (See here for a good reference on the early work on pyruvate carboxylase). Its discovery was very controversial because at the time it was thought that animal/bacterial cells could not 'fix' CO2; that is it was though that CO2 is only 'fixed' in photosynthesis. This discovery disproved that piece of dogmatism.
A third enzyme that requires CO2 as substrate (in the form of bicarbonate) is propionyl-CoA carboxylase. This enzyme occurs in mitochondria and functions in odd-chain fatty acid metabolism. It also contains biotin.
I have concentrated on some biochemical aspects of your question. The three enzymes mentioned, acety-CoA carboxylase, pyruvate carboxylase and propionyl-CoA carboxylase all require CO2 in the form of bicarbonate as substrate, all contain biotin, and (as far as I am aware) all play very central roles in mammalian metabolism. (They also all require ATP as substrate).
Of the many interesting aspects of biotin, I'll mention just one. Egg white contains a protein, avidin, which binds biotin very, very tightly. In fact the biotin-avidin interaction is one of the strongest non-covalent interactions known. As far as I am aware, no-one knows the function of avidin in egg white. Some bacteria contain a similar (but evolutionarily unrelated) protein called streptavidin. No one knows the function of steptavidin either (again, as far as I am aware).
The original Wood & Werkman paper: was published in the the Biochemical Journal in 1936
The utilisation of CO2 in the dissimilation of glycerol by the propionic acid bacteria.
Harland Goff Wood and Chester Hamlin Werkman.
Biochemical Journal, Volume 30, January 1936, pp 48-53
To add my 2 cents worth: Breathing rate and depth is regulated by chemoreceptors in the medulla. These chemoreceptors primarily respond to pH of the blood, but the pH is for an important part determined by the CO2/HCO3- equilibrium as explained by @TomD. Essentially it is the increase in CO2 that is sensed by the medulla and which increases breathing frequency and the depth of inhalation. See this web page about respiratory control.
Some additional points about role of bicarbonate (which is directly formed from carbon dioxide as described by TomD):