The Dow Jones Industrial Average (DJIA) is a Price-weighted index. That means that the index is calculated by adding up the prices of the constituent stocks and dividing by a constant, the "Dow divisor". (The value of the Dow divisor is adjusted from time to time to maintain continuity when there are splits or changes in the roster.) This has the curious effect of giving a member of the index influence proportional to its share price. That is, if a stock costing $100 per share goes up by 1%, that will change the index by 10 times as much as if a stock costing $10 per share goes up by the same 1%.
Now look at the price of Google. It's currently trading at just a whisker under $700 per share. Most of the other stocks in the index trade somewhere between $30 and $150, so if Google were included in the index it would contribute between 5 and 20 times the weight of any other stock in the index. That means that relatively small blips in Google's price would completely dominate the index on any given day.
Until June of 2014, Apple was in the same boat, with its stock trading at about $700 per share. At that time, Apple split its stock 7:1, and after that its stock price was a little under $100 per share. So, post-split Apple might be a candidate to be included in the Dow the next time they change up the components of the index. Since the Dow is fixed at 30 stocks, and since they try to keep a balance between different sectors, this probably wouldn't happen until they drop another technology company from the lineup for some reason. (Correction: Apple is in the DJIA and has been for a little over a year now. Mea culpa.)
The Dow's price-weighting is unusual as stock indices go. Most indices are weighted by market capitalization. That means the influence of a single company is proportional to its total value. This causes large companies like Apple to have a lot of influence on those indices, but since market capitalization isn't as arbitrary as stock price, most people see that as ok. Also, notice that I said "company" and not "stock". When a company has multiple classes of share (as Google does), market-cap-weighted indices include all of the share classes, while the Dow has no provision for such situations, which is another, albeit less important, reason why Google isn't in the Dow. (Keep this in mind the next time someone offers you a bar bet on how many stocks are in the S&P 500. The answer is (currently) 505!)
Finally, you might be wondering why the Dow uses such an odd weighting in its calculations. The answer is that the Dow averages go back to 1896, when Charles Dow used to calculate the averages by hand. If your only tools are a pencil and paper, then a price-weighted index with only 30 stocks in it is a lot easier to calculate than a market-cap-weighted index with hundreds of constituents.
About the Dow Jones Averages.
Dow constituents and prices
Apple's stock price chart. The split in 2014 is marked. (Note that prices before the split are retroactively adjusted to show a continuous curve.)