I feel that Mega Evolutions serve a dual purpose:
The first is to satisfy both the crowds who want new evolutions of old Pokémon, as well as those wanting old final stage Pokémon as "the final product", "the peak of the mountain" or "the end of the line", or whatever metaphor would fit here. If you want powerful Pokémon for an in-game run, first stage 'mons can be (somewhat cynically) regarded as "transition stages" before the creature you caught reaches its final power stage. Rhydon, Magneton and Magmar, among many others, used to be at the epitome of their evolutionary families. They were the strongest form of the base Pokémon, key players to consider when building a good team. To put it bluntly, you caught a Rhyhorn to get a Rhydon for use in your team. The final evolution was the goal you aimed for when catching and training base forms.
However, Gen. IV came around, and suddenly Rhydon, Magneton and Magmar found themselves halfway down the hill again. Suddenly, they were the transitional stages. A mid-project goal reached on the way towards final evolution and strategic viability. Now, players caught Rhyhorn, Magnemite and Magby with other goals in mind. Rhyperior, Magnezone and Magmortar, those were the names at the end of the line, the powerful final evolutions. Old fan favourites Rhydon, Magneton and Magmar were pushed back to a transitional stage, a pupae between the first and final evolution. Some fans didn't take that very well. However, many other fans wanted their favourite evolution lines to join the fun too. Pokémon such as Dunsparce, Farfetch'd and Chimecho were weak and unviable beyond all repair. Only a new evolutionary stage could make these 'mons relevant again, and add enough power to make them a desirable addition to a team (if only by being temporary stages while waiting for the kickass final evolution).
Mega Evolutions let the end of the line stay where it is, while granting a power boost similar to evolution. For all intents and purposes, Mega Evolution is akin to a regular evolution. There's a design overhaul, stats are given a solid boost, abilities sometimes change... but the name of the relevant Pokémon stays the same. Arcanine (just a fictional example, a MEvo is neither confirmed nor even implied) is still the king of its evolutionary line, the monster you have in mind when you decide to catch a Growlithe (still an example). However, whereas Arcanine is a little too weak to meet the standards of top-tier competitive gaming, Mega Arcanine has all the required power and then some. But Mega Arcanine is just a temporary form of Arcanine, when you travel with it and call it to battle, it is still an Arcanine. There is no evolutionary tier above it to steal its spotlight. Arcanine remains its old, marketable, fan-favourite self, while also gaining enough power to play with the "big boys".
The second purpose is, of course, marketability. Giving old fan favourites even more power, relevancy and appeal, bringing them out from the depths of forgettability they have sunken into over the years. "Remember your good old friend Blaziken? It kicks even more ass now!". Lucario, which was very well received by the consumers, is given more spikes, fur and power and sent back to capture the hearts of even more boys. Charizard, all-time fan favourite, is a joke in competitive battling, they say? Let's shove a ton of new tools onto it, until it is viable and relevant again. Pokémon previously considered "untouchable", being at the end of their evolutionary lines or even Legendary, can still have their power levels raised, to wild applause from the fans who want them to be among the most powerful Pokémon of them all (newcomers to Smogon usually express this as "I want it to be OU"). GameFreak adds bells and whistles, raise the stats and dish out desirable abilities, in a deliberate attempt to make the most popular Pokémon simultaneously be the most powerful ones.
Do I dislike it? Not yet, we haven't seen the full effect of Mega Evolutions on (competitive) gameplay yet. We still haven't seen how the bulk of the fans react to the power boosts. If Mega Pokémon in the long term end up being totally dominating, in competitive play as well as marketing, I'll probably end up disliking it. That would imply a deliberate attempt towards steering the spotlight over to certain Pokémon at the expense of many of the rest, and favouring raw power over the surprisingly intricate strategies the Pokémon games open up for. Instead of making the middle-stage Pokémon irrelevant, it will make all non-Mega Pokémon irrelevant.
On the other hand, if Mega Evolutions are treated with some modesty, being just another strategy available for use, I think I might like it a bit. I hope I can wait to pass judgment until the end of this generation. It will take a lot of time to see the overall impact of Mega Evolutions.