Several articles in late 2013 said that rents in LA are rising 10% a year. ,  According to the city, because it's based on higher-end apartments, the prices are overstated. Some stats debunkers also refute it . More on this later.
Loopnet, a commercial real estate listing site, indicates that the prices that rentals are selling for has been increasing rapidly. In 2013, the average price of a single unit in a multi-unit apartment (listed on loopnet) has risen from 150k to 170k, or a 13% increase - so the price to buy an apartment unit has risen faster than the rent.
The City's explanation about how the data is collected might indicate that some stats aren't showing real trends. According to a couple apartment listing sites, which base stats on their listings, which tend to be for upper-end apartments, rents are rising around 5% every six months. ,  More significantly, the highest rent areas now include the entire Downtown area (including South Park, which is the highest rent), and around Hollywood. These were low rent areas since the 1960s (or before in most areas). New construction is raising the rents in these neighborhoods. So the rise in rents has been far more dramatic.
The spreading gentrification may be the reasons for the rise in the price of apartments being sold.
These are just rumors, but I have heard that apartments and houses are being bought up in all-cash deals, bypassing the banks. As the rich have gotten richer, they have invested in companies that buy rental real estate. Besides causing prices to rise, these all-cash buyers are able to sometimes buy at the asking price or below, because it's less hassle for the seller to sell a building when banks aren't involved. For owners who aren't using an agent, the savings is even greater - so there are probably offers and deals being made that never reach the listings. Would-be pettit bourgeois mom-and-pop landlords are going to be replaced by investment companies and professional management companies.
In Marxian terms, this is the continuation of capital consolidation. There is a capital surplus and it continues to be invested into cities. The crisis was a downturn that will ultimately only accelerate the process of immiseration of the exurb, impoverishment of many suburbs, and capital accumulation into the urban core.
For many of us, this will feel like a looming crisis, but just as yesterday's capital conditions prefigured today's current conditions, the current rise in prices and consolidation of capital will lead to a rental crisis. So I will talk of the crisis in the present tense.
The social democrat response to this crisis, at least in Los Angeles, is nonprofit affordable housing.  We need more. Not only does nonprofit affordable housing create housing, it creates jobs, and it does it primarily by making a civic demand on the wealthy.
The Neoliberal Present and Some of Its History
However, amidst this demand for more nonprofit housing, we're seeing the destruction of public housing. The destruction of public housing is a barely-seen trend in LA, because there's so little public housing, but it's happening due to HOPE-VI, which declared large scale public housing a kind of social problem, and mandated its destruction and rebuilding as a mix of public housing and market-rate housing with an architecture more reminiscent of suburban housing.
The standard example in LA is the teardown of Aliso Pico and it's replacement with Pueblo Del Sol. Was this good or bad? It's a mixed bag. There was good and bad, but what's done is done. What it portends, however, is a general decrease in public housing, and a hostility to the very idea of public housing. (Projects targeted for either destruction or conversion include but are not limited to Ramona Gardens, Nickerson Gardens, William Mead.)
Neoliberalism is in a long fight over public housing, and in LA the most notable story about it is Chavez Ravine, where the Dodgers play. The original plan was to tear down the existing "blighted" community and replace it with high rise public housing. With the power of the city, eminent domain was used to buy up most of the homes in Chavez Ravine. The community was torn down, but landlord groups mobilized to prevent the erection of public housing. They were afraid, justifiably, that public housing would compete with their private apartments, and cause prices to drop.
The landlords won, and the new public housing was not built. (Later, the land was given to the Dodgers in trade for land around the old Wrigley Field in south central.)
Renters wouldn't see a big victory until the 1978 Rent Stabilization Ordinance (RSO) that would introduce some rent control in to LA.
In the UK, our sibling in Europe, there's a tradition of public housing, but with Thatcherism, public housing has been privatized with residents being sold their units. While, to us Americans, that looks like a great deal, if you really consider that public housing is already owned by the people, it's not such a great deal. A buyer is now locked into staying at the same apartment. With capital accumulation now re-centered on the homeowners, the desire for profit is spread to the community, and it's inevitable that over time, there will be price inflation for these apartments, and also widespread political pressure to prevent the construction of more public housing.
Eventually, as the apartments become decrepit, there's the potential for capitalist consolidation of housing. All the existing owners can be bought out, and the apartments rebuilt, and then rented out by the new owners.
With the increase in crisis in Los Angeles, organizing around housing will be both more necessary and easier. Radicals and progressives should plan on this. Study up on the RSO, county, and state laws, and spread the knowledge.
Support nonprofit affordable housing, even if it exists within the "nonprofit industrial complex." People are in need, and the alternative is to totally decimate the poor and working class and relegate them to the edges of the cities (like the French banleiues) where they will be ignored (even more than they are ignored today because they are in conflict with gentrification).
Support "right to the city" groups that engage in practical tactics to retain housing for working class communities. Many exist: CAN, CES, UNIDAD, Union de Vecinos. Please add more in the comments.
Always get an apartment inspection from the LAHD. If there are sufficient code violations, you can have your rent reduced, or make a stronger demand to have the apartment repaired.
If you are able to risk conflict with landlords, demand repairs. This causes the profitability of units to decline, making them less appealing to investors.
Have more ideas? Add comments.
Practical Utopian Strategies
Develop ways to promote the idea of public housing. It's basically politically impossible to push for public housing at this time, due to the overwhelming power of neoliberal forces, but the idea of public and commune housing can be promoted.
Learn adverse possession, and consider it. The right to squat doesn't really exist in LA, but what few rights we have, we need to keep. Pushing for the expansion of squatters rights is a utopian strategy.
Housing as a right. In the US and especially in LA, people don't consider housing a right. The punishment for poverty is homelessness. The immorality of the status quo must be fought.
Housing co-ops and trusts are a practical response, but are not going to benefit anyone except the people within the co-op. To address the crisis, it must be done at the city, county, and state level. If a co-op has any pretense to progressivism, it should support expansion of co-ops.
A group of people renting a house is not a co-op. It's just a group of renters buying housing in bulk.
In closing, please, just see through your situation with trenchant analysis, and know where you are, and figure out how you're going to fight for all peoples right to a home.